Answer
$x=\frac{4}{5}$
Work Step by Step
Note that $32=2^5$ so the given equation is equivalent to:
$2^{5x+1}=2^5$
Using the rule $a^m=a^n\longrightarrow m=n$ gives:
$5x+1=5$
$5x=4$
$x=\frac{4}{5}$
Check:
$2^{5x+1}=32$
$2^{5*\frac{4}{5}+1}=32$
$2^{4+1}=32$
$2^{5}=32$
$32=32$
Thus, the answer is correct.