Five Fives/Table of 5s

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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})} } $

$ 4 = \dfrac{ \ln{5} }{ \ln{\left( \sqrt{ \sqrt{ 5 } } \right) } } $

$ 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 $

$ 12696403353658275925965100847566516959580321051449436762275840000000000000 = 55! $

Three 5s

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

$ \dfrac{24}{25} = \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)} $

$ 5 = 5 - 5 + 5 $

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

$ 20 = \dfrac{ 5 \lg{5} }{ \lg{\left(\sqrt{\sqrt{5}}\right)} } $

$ 30 = 5 \times 5 + 5 $

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

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

$ 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 $

$ 3125 = \dfrac{5 \times 5^5}{5} $