$\begin{array}{l}
\sin \left( {x + 1} \right) = \sin 5x\\
\Leftrightarrow \left[ \begin{array}{l}
5x = x + 1 + k2\pi \\
5x = \pi - x - 1 + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{1}{4} + \dfrac{{k\pi }}{2}\\
x = \dfrac{\pi }{6} - \dfrac{1}{6} + \dfrac{{k\pi }}{3}
\end{array} \right.\left( {k \in \mathbb{Z}} \right)
\end{array}$
