Answer
Error: equating the exponents when the bases are not the same
Correct solution: $x=-18$
Work Step by Step
The error is in equating the exponents when the bases are not the same (one is $5$ and the other is $25$).
To correctly solve, we must first make the bases same.
Rewriting $25$ as $5^{2}$, we have
$5^{3x+2}=(5^{2})^{x-8}$
$\implies 5^{3x+2}=5^{2x-16}$
Now, equating the exponents, we have
$3x+2=2x-16$
Solving for $x$, we obtain
$3x-2x=-16-2$
$x=-18$
