**SOLUTION —**

$y=5 \cos x-3 \sin x$

$\begin{array}{l}\Rightarrow \quad \frac{d y}{d x}=-5 \sin x-3 \cos x \\\Rightarrow \quad \frac{d^2 y}{d x^2}=-5 \cos x+3 \sin x \\\therefore \quad \frac{d^2 y}{d x^2}+y=-5 \cos x+3 \sin x+5 \cos x-3 \sin x=0\end{array}$

So, The correct option will be **(D).**