Answer
$x=-1$
Work Step by Step
First, we let
$\log_{5}{\frac{1}{5}} = x$
RECALL:
$\log_b{y} =x \longrightarrow b^x=y$
Use the rule above, where $y=\frac{1}{5}$ and b=5, to obtain:
$5^x=\frac{1}{5}$
Write $\frac{1}{5}$ as $ 5^{-1}$ to obtain:
$5^x=5^{-1}$
Use the rule "If $a^x=a^y$, then $x=y$" to obtain:
$x=-1$
