$\operatorname{Sin}(\frac{5\pi }{2}+x)=\operatorname{Cos}x,\sqrt{2}\operatorname{Sin}(\frac{\pi }{4}-x)=\operatorname{Cos}x-\operatorname{Sin}x\Rightarrow \operatorname{Cos}x-\operatorname{Sin}x=1+\operatorname{Cos}x\Rightarrow \operatorname{Sin}x=-1\to x=2k\pi -\frac{\pi }{2}$