Answer
$\frac{1}{5}\tan 5x+C$
Work Step by Step
Use the substitution $u=5x$. Then $du=5dx$, so $dx=\frac{1}{5} du$.
$\int\sec^2 5x dx$
$=\int \sec^2 u*\frac{1}{5}du$
$=\int \frac{1}{5}\sec^2 udu$
$=\frac{1}{5}\tan u+C$
$=\frac{1}{5}\tan 5x+C$