\(\Leftrightarrow sin4x=-cos5x\)
\(\Leftrightarrow sin4x=sin\left(5x-\frac{\pi}{2}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}5x-\frac{\pi}{2}=4x+k2\pi\\5x-\frac{\pi}{2}=\pi-4x+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{2}+k2\pi\\x=\frac{\pi}{6}+\frac{k2\pi}{9}\end{matrix}\right.\)