Row-reduce the augmented matrix representing this system, to find
\begin{equation*}
\begin{bmatrix}
\leading{1} & -2 & 0 & 6 & 0 & 1\\
0 & 0 & \leading{1} & -4 & 0 & 3\\
0 & 0 & 0 & 0 & \leading{1} & -5\\
0 & 0 & 0 & 0 & 0 & 0
\end{bmatrix}
\end{equation*}
The system is consistent (no pivot column in column 6, Theorem RCLS). $x_2$ and $x_4$ are the free variables. Now apply Theorem VFSLS directly, or follow the three-step process of Example VFS, Example VFSAD, Example VFSAI, or Example VFSAL to obtain
\begin{equation*}
\colvector{x_1\\x_2\\x_3\\x_4\\x_5}
=
\colvector{1\\0\\3\\0\\-5}+
x_2\colvector{2\\1\\0\\0\\0}+
x_4\colvector{-6\\0\\4\\1\\0}
\end{equation*}