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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

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

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

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

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

$10 = 5 + 5$

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

$25 = 5 \times 5$

$125 = 5! + 5$

$600 = 5 \times 5!$

$3125 = 5^5$

## 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

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

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

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

$20 = 5 + 5 + 5 + 5$

$50 = 5 \times 5 + 5 \times 5$

$130 = 5 \times 5 \times 5 + 5$

$120 = 5 \times 5 \times 5 - 5$