Answer
$2\sin 4x\cos x$
Work Step by Step
Use the first Sum-to-Product Formula, $\sin x+\sin y=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}$.
$\sin 5x+\sin 3x$
$=2\sin\frac{5x+3x}{2}\cos\frac{5x-3x}{2}$
$=2\sin\frac{8x}{2}\cos\frac{2x}{2}$
$=2\sin 4x\cos x$