Let $f(x) = x^4(5 \sin x-3 \cos x)$$

By product rule,

$f'(x) = x^4\large\frac{d}{dx}$$(5 \sin x - 3 \cos x)+(5 \sin x - 3 \cos x)\large\frac{d}{dx}$$(x^4)$

$ x^4 \bigg[5 \large\frac{d}{dx}$$\sin x-3 \large\frac{d}{dx}$$\cos x \bigg]+(5 \sin x - 3 \cos x)\large\frac{d}{dx}$$(x^4)$

$x^4 [5 \cos x -3(-\sin x)]+(5 \sin x-3 \cos x)(4x^3)$

$x^3 [5x \cos x+ 3x \sin x+20 \sin x-12 \cos x]$