Answer
$$
5^{-|x|} =\frac{1}{25}
$$
The solution of the given equation is
$$
x =2 \text { or } x=-2
$$
Work Step by Step
$$
5^{-|x|} =\frac{1}{25}
$$
Since the bases must be the same, write $ \frac{1}{25} $ as $5^{-2 }$ and 64 as $ 2^{6} $ giving
$$
\begin{aligned} 5^{-|x|} &=\frac{1}{25} \\ 5^{-|x|} &=5^{-2 } \\-|x| &=-2 \\ x &=2 \text { or } x=-2 \end{aligned}
$$
So, the solution of the given equation is
$$
x =2 \text { or } x=-2
$$
