Answer
Solution set = $\{5\}.$
Work Step by Step
$ 5^{2-x}=\displaystyle \frac{1}{125} \qquad $... Recognize 125 as a power of 5
$ 5^{2-x}=\displaystyle \frac{1}{5^{3}} \qquad $... apply $ a^{-n}=\displaystyle \frac{1}{a^{n}}$
$ 5^{2-x}=5^{-3}\qquad $... if $ a^{m}=a^{n}$, then $ m=n $
$ 2-x=-3\qquad $... add $ x+3$
$2+3=x $
$ x=5$
Solution set = $\{5\}.$
