$$\frac{\sqrt{4+x}-2}{\sin\ 5x}=$$
$\frac{\sqrt{x+4}-2}{\sin(5x)}$
$\frac{-10x\cos(5x)+20\sqrt{x+4}\cos(5x)+\sin(5x)-40\cos(5x)}{2\sqrt{x+4}\left(\sin(5x)\right)^{2}}$
