Answer
$\left\{-4\right\}$
Work Step by Step
Expressing both sides of the given equation, $
5^x=\dfrac{1}{625}
,$ in the same base results to
\begin{align*}\require{cancel}
5^x&=\dfrac{1}{5^4}
\\\\
5^x&=5^{-4}
.\end{align*}
Since $b^x=b^y$ implies $x=y$, the equation above implies
\begin{align*}\require{cancel}
x&=-4
.\end{align*}
Hence, the solution set of the equation $
5^x=\dfrac{1}{625}
$ is $
\left\{-4\right\}
$.
