Answer
The solution set is $\left\{8\right\}$.
Work Step by Step
Subtract $2x$ and subtract $5$ from both sides.
$3x+5-2x-5=2x+13-2x-5
\\x=8$
Check:
$3(8)+5\stackrel{?}{=}2(8)+13
\\24+5\stackrel{?}{=}16+13
\\29 \stackrel{\checkmark}{=}29$
The solution set is $\left\{8\right\}$.