Answer
The system is inconsistent.
Work Step by Step
$\left\{\begin{array}{lllll}
2x & -3y & -z & =0 & \\
-x & +2y & +z & =5 & /R_{2}=r_{2}+r_{1}\\
3x & -4y & -z & =0 & /R_{3}=r_{3}-r_{1}
\end{array}\right.$
... Eliminate z in eq. 2 and 3
$\left\{\begin{array}{lllll}
2x & -3y & -z & =0 & \\
x & -y & & =5 & \\
x & -y & & =0 & /R_{3}=r_{3}-r_{2}
\end{array}\right.$
... Eliminate y in equation 3
$\left\{\begin{array}{lllll}
2x & -3y & -z & =0 & \\
x & -y & & =5 & \\
& & 0 & =-5 &
\end{array}\right.$
The third equation is impossible - there are no solutions.
The system is inconsistent.