#### Answer

$x=1$
or
The solution set is: $\{1\}$.

#### Work Step by Step

The term $125$ can be written as: $125=5^3$
So, the given equation can be equivalent to $5^{x+2}=5^3$
Recall the rule that $a^m=a^n \longrightarrow m=n$ if $a\ne1,a\ne-1$
Applying this rule, we obtain:
$5x+2=5^3 \\ x +2=3$
Simplify this equation to obtain:
$x+2=3 \\ (x+2)−2=3−2 \\ x=1$
So, the solution set is: $\{1\}$