\(\Leftrightarrow cos5x=-sin3x\)
\(\Leftrightarrow cos5x=cos\left(\dfrac{\pi}{2}+3x\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=\dfrac{\pi}{2}+3x+k2\pi\\5x=-\dfrac{\pi}{2}-3x+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+k\pi\\x=-\dfrac{\pi}{16}+\dfrac{k\pi}{4}\end{matrix}\right.\)