\[\begin{array}{l}
\,\,\,\,\,\,\,\cos \left( {x - 5} \right) = \frac{{\sqrt 3 }}{2},\,\,\,x \in \left( { - \pi ;\,\,\,\pi } \right)\\
\Leftrightarrow \cos \left( {x - 5} \right) = \cos \frac{\pi }{6}\\
\Leftrightarrow \left[ \begin{array}{l}
x - 5 = \frac{\pi }{6} + k2\pi \\
x - 5 = - \frac{\pi }{6} + m2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{\pi }{6} + 5 + k2\pi \\
x = 5 - \frac{\pi }{6} + m2\pi
\end{array} \right.\,\,\,\,\,\left( {k,\,\,m \in Z} \right)\\
x \in \left( { - \pi ;\,\,\pi } \right) \Rightarrow \left[ \begin{array}{l}
- \pi < \frac{\pi }{6} + 5 + k2\pi < \pi \\
- \pi < 5 - \frac{\pi }{6} + m2\pi < \pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
- \frac{{7\pi }}{6} - 5 < k2\pi < \frac{{5\pi }}{6} - 5\\
- \frac{{5\pi }}{6} - 5 < m2\pi < \frac{{7\pi }}{6} - 5
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
- 1,4 < k < - 0,379\\
- 1,2 < m < - 0,2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
k = 0\\
m \in \emptyset
\end{array} \right. \Rightarrow x = \frac{\pi }{6} + 5.
\end{array}\]
