From charlesreid1

Back to Five Fives

One 5

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


5^{\frac{1}{2}} = \sqrt{5}


5 = 5


120 = 5!


Two 5s


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


1 = \dfrac{5}{5}


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


5 = \sqrt{5 \times 5}


10 = 5 + 5


24 = \dfrac{5!}{5}


25 = 5 \times 5


125 = 5! + 5


600 = 5 \times 5!


3125 = 5^5

Three 5s


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


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


5 = 5 - 5 + 5


4 = 5 - \dfrac{5}{5}


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


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


15 = 5 + 5 + 5


20 = 5 \times 5 - 5


30 = 5 \times 5 + 5


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


625 = \dfrac{5^5}{5}


Four 5s


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


1 = \dfrac{5^5}{5^5}


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


20 = 5 + 5 + 5 + 5


50 = 5 \times 5 + 5 \times 5


130 = 5 \times 5 \times 5 + 5


120 = 5 \times 5 \times 5 - 5