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