\[\begin{array}{l}
4\cos x - 2\sqrt 3 \sin x = 5\\
\Leftrightarrow \frac{4}{5}\cos x - \frac{{2\sqrt 3 }}{5}\sin x = 1\\
\Leftrightarrow \cos \left( {x + \alpha } \right) = 1\,\,\,\,\,\left( {\cos \alpha = \frac{4}{5};\,\,\,\sin \alpha = \frac{{ - 2\sqrt 3 }}{5}} \right)\\
\Leftrightarrow x + \alpha = k2\pi \\
\Leftrightarrow x = - \alpha + k2\pi \,\,\,\left( {k \in Z} \right).
\end{array}\]
