$\operatorname{Sin}5x(\operatorname{Cos}3x-\operatorname{Sin}5x)+\operatorname{Cos}5x(\operatorname{Sin}3x-\operatorname{Cos}5x)=0$

$\Rightarrow \operatorname{Sin}5x\operatorname{Cos}3x-{{\operatorname{Sin}}^{2}}5x+\operatorname{Cos}5x\operatorname{Sin}3x-{{\operatorname{Cos}}^{2}}5x=0$

$\Rightarrow \operatorname{Sin}5x\operatorname{Cos}3x+\operatorname{Cos}5x\operatorname{Sin}3x={{\operatorname{Sin}}^{2}}5x+{{\operatorname{Cos}}^{2}}5x=1$

$\Rightarrow \operatorname{Sin}(5x+3x)=1\Rightarrow \operatorname{Sin}8x=1\to 8x=2k\pi +\frac{\pi }{2}\Rightarrow x=\frac{k\pi }{4}+\frac{\pi }{16}$