Answer
$x=2$
Work Step by Step
Note that $25=5^2$. Thus, the given equation is equivalent to:
$\left(\dfrac{1}{5}\right)^x = \dfrac{1}{5^2}
\\\left(\dfrac{1}{5}\right)^x = \left(\dfrac{1}{5}\right)^2$
Use the rule $a^m=a^n \longrightarrow m = n$ to obtain:
$x=2$