$_{5\operatorname{Sin}x+3\operatorname{Cos}(\frac{3\pi }{2}-x)=1\Rightarrow 5\operatorname{Sin}x-3\operatorname{Sin}x=1\Rightarrow 2\operatorname{Sin}x=1\Rightarrow \operatorname{Sin}x=\frac{1}{2}=\operatorname{Sin}\frac{\pi }{6}\Rightarrow \left\{ _{x=2k\pi +(\pi -\frac{\pi }{6})=2k\pi +\frac{5\pi }{6}}^{x=2k\pi +\frac{\pi }{6}}\Rightarrow x=2k\pi +\frac{i\pi }{6},i\in \left\{ 1,5 \right\} \right.}^{\operatorname{Cos}(\frac{3\pi }{2}-x)=-\operatorname{Sin}x}$