Answer
$x\approx0.97$
Work Step by Step
Isolate the $e$ term and then use the natural log on both sides. Then solve for $x$.
$e^{5x}-32=96$
$e^{5x}=128$
$\ln(e^{5x})=\ln(128)$
$5x=\ln(128)$
$x=\frac{\ln(128)}{5}$
$x\approx0.97$