Answer
$\{1\}$
Work Step by Step
Note that $125=5^3$.
Thus, the given equation is equivalent to $5^{x+2}=5^3.$
RECALL:
If $a\ne1$ and $a\ne-1$ then $a^x=a^y\longrightarrow x=y$
Hence,
$5^{x+2}=5^3 \longrightarrow x+2=3$
Solve the equation above to obtain
$x+2=3\\
(x+2)-2=3-2\\
x=1$
The solution set is:$\{1\}.$
