Five Fives/Table of 5s

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Zero 5s

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 1=\ln {e}}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 9+4{\sqrt {5}}=\phi \left(\phi ^{5}\right)}

One 5

Various ways of arranging a single 5 to yield different numbers. (More limited than 4, of course...)

${\sqrt {5}}$

$\phi ^{n}{\sqrt {5}}=\phi ^{n+1}+\phi ^{n-1}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle -1=\cos {\left(5\pi \right)}}

$0=\sin {\left(5\pi \right)}$

$1=x^{\sin {\left(5\pi \right)}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 2=\phi \times \phi \times \phi -{\sqrt {5}}}

$5$

$15=5!!$

$120=5!$

Two 5s

$0=\ln {\dfrac {5}{5}}$

$1={\dfrac {5}{5}}$

$2={\dfrac {\ln {(5)}}{\ln {({\sqrt {5}})}}}$

$3=\phi ^{5}-5\phi$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 4={\dfrac {\ln {5}}{\ln {\left({\sqrt {\sqrt {5}}}\right)}}}}

$5={\sqrt {5\times 5}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 8={\dfrac {\ln {5}}{\ln {\left({\sqrt {\sqrt {\sqrt {5}}}}\right)}}}}

$10=5+5$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 11=\phi ^{5}-\phi ^{-5}}

$16={\dfrac {\ln {5}}{\ln {\left({\sqrt {\sqrt {\sqrt {\sqrt {5}}}}}\right)}}}$

$24={\dfrac {5!}{5}}$

$25=5\times 5$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 32={\dfrac {\ln {5}}{\ln {\left({\sqrt {\sqrt {\sqrt {\sqrt {\sqrt {5}}}}}}\right)}}}}

$55$

$115=5!-5$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 125=5!+5}

$600=5\times 5!$

$3125=5^{5}$

$11981655542024930675232002=\phi ^{5!}-\phi ^{-5!}$

$12696403353658275925965100847566516959580321051449436762275840000000000000=55!$

Three 5s

${\dfrac {1}{2}}={\dfrac {\ln {\left({\dfrac {5}{\sqrt {5}}}\right)}}{\ln {(5)}}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\dfrac {3}{5}}={\dfrac {1}{5}}\left(\phi ^{5}-5\phi \right)}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\dfrac {25}{24}}={\dfrac {5!+5}{5!}}}

$1={\dfrac {\sqrt {5\times 5}}{5}}$

$2={\dfrac {\ln {(5)}}{\ln {\left({\dfrac {5}{\sqrt {5}}}\right)}}}$

$3=\log _{5}{(5!+5)}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 4=5-{\dfrac {5}{5}}}

$5=5-5+5$

$5={\sqrt[{5}]{5^{5}}}$

$5={\sqrt {\dfrac {\sqrt {5^{5}}}{\sqrt {5}}}}$

$5={\dfrac {5\times 5}{5}}$

$6=5+{\dfrac {5}{5}}$

$7=5+{\dfrac {\ln {\left(5\right)}}{\ln {\left({\sqrt {5}}\right)}}}$

$8=\phi ^{5}-5\phi +5$

$9=5+{\dfrac {\ln {\left(5\right)}}{\ln {\left({\sqrt {\sqrt {5}}}\right)}}}$

$10={\sqrt {5}}\left({\sqrt {5}}+{\sqrt {5}}\right)$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 11={\dfrac {55}{5}}}

$12={\dfrac {5!}{5+5}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 13=5!!-{\dfrac {\ln {\left(5\right)}}{\ln {\left({\sqrt {5}}\right)}}}}

$15=5+5+5$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 16=\phi ^{5}-\phi ^{-5}+5}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 18=5!!+\phi ^{5}-5\phi }

$19={\dfrac {5!}{5}}-5$

$20=5\times 5-5$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 20={\dfrac {5\lg {5}}{\lg {\left({\sqrt {\sqrt {5}}}\right)}}}}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 25={\dfrac {5!+5}{5}}}

$25={\dfrac {\sqrt {5^{5}}}{\sqrt {5}}}$

$25={\sqrt {5}}\left(\phi ^{5}+\phi ^{-5}\right)$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 25=5+5+5!!}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 26=\left(\phi ^{5}-\phi {-5}\right)+5!!}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 29={\dfrac {5!}{5}}+5}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 30=5\times 5+5}

$32=\left({\dfrac {\ln {5}}{\ln {\sqrt {5}}}}\right)^{5}$

$50=55-5$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 50=5(5+5)}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 55=5\left(\phi ^{5}-\phi ^{-5}\right)}

$60={\dfrac {5!}{\left({\dfrac {\ln {5}}{\ln {\sqrt {5}}}}\right)}}$

$95=5!-5\times 5$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 96=5!-{\dfrac {5!}{5}}}

$110=5!-5-5$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 120=5!+5-5}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 123=\phi ^{5}-5\phi +5!}

$130=5!+5+5$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 145 = 5! + 5 \times 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 243 = \left( \phi^{5} - 5 \phi \right)^5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 625 = \dfrac{5^5}{5} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1024 = \left( \dfrac{ \ln{5} }{ \ln{ \sqrt{ \sqrt{5} } } } \right)^5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3005 = 5^5 - 5! }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 9765625 = \left( 5 \times 5 \right)^5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 503284375 = 55^5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 298023223876953125 = 5^{5 \times 5} }

Four 5s

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1 = \dfrac{ \ln{ \left( \dfrac{5}{ \sqrt{5} } \right) } + \ln{5} }{ \ln{5} } }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1 = \dfrac{5^5}{5^5} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1 = \dfrac{ 5 \times 5}{5 \times 5} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 6 = \dfrac{ \ln{(5)} }{ \ln{(\sqrt{5})} } + \dfrac{ \ln{(5)} }{ \ln{(\sqrt{\sqrt{5}})} } }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 7 = \sqrt{ \dfrac{5!}{5} + (5 \times 5) } }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 8 = \left( \dfrac{ \ln{(5)} }{ \ln{(\sqrt{5})} } \right) \left( \dfrac{ \ln{(5)} }{ \ln{(\sqrt{\sqrt{5}})} } \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 9 = 5 + 5 - \dfrac{5}{5} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 11 = 5 + 5 + \dfrac{5}{5} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 12 = \left( \dfrac{5!}{5} \right) \times \left( \dfrac{ \ln{\sqrt{5}} }{ \ln{5} } \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 13 = \dfrac{5! - 55}{5} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 15 = \left( \log_{5}{ (5! + 5)^5 } \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 20 = 5 + 5 + 5 + 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 26 = \dfrac{5^5 - 5}{5!} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 34 = \phi^{5 + 5} - 55 \phi }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 35 = \dfrac{55 + 5!}{5} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 35 = 5 \times 5 + 5 + 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 49 = \dfrac{5!}{5} + (5 \times 5) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 50 = 5 \times 5 + 5 \times 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 52 = 55 - \phi^{5} + 5 \phi }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 60 = 5 \left( \dfrac{ 5! }{ 5 + 5 } \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 70 = 5! + 5 - 55 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 89 = \dfrac{ \phi \left( \phi^{5 + 5} \right) - 55 }{ \phi } }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 120 = 5 \times 5 \times 5 - 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 123 = \phi^{5+5} + \dfrac{1}{\phi^{5+5}} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 125 = 5 \sqrt{5} \left( \phi^{5} + \phi{-5} \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 130 = 5 \times 5 \times 5 + 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 140 = 5! + (5 \times 5) - 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 150 = 5 \left( 5 \times 5 + 5 \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 160 = 5 \left( \dfrac{ \ln{5} }{ \ln{\sqrt{5}} } \right)^5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 243 = \left( \log_{5}{(5! + 5)} \right) ^5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle ( 5_{5} )! = (10_{5})! = 440_{5} = 120_{10} }

(5 base 5 is 10 base 5; 5 base 5 factorial is 440 base 5, or 120 base 10. No surprises here.)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 505 = \dfrac{5^5}{5} - 5! }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 605 = 55 \left( \phi^5 - \phi^{-5} \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3000 = \left( 5^5 - 5 \right) - 5! }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3025 = 55 \times 55 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3070 = 5^5 - 55 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3100 = 5^5 - 5 \times 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3125 = \dfrac{5 \times 5^5}{5} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 161051 = 11^5 = \left( \dfrac{55}{5} \right)^5 }