The augmented matrix

\begin{equation*} \begin{pmatrix} 1 & 5 & 2 & -6 \\ 0 & 4 & -7 & 2 \\ 0 & 0 & 0 & 5 \end{pmatrix} \end{equation*}

represents an inconsistent system, for per the last row

\begin{align*} (x_1, x_2, x_3) & = (0, 0, 0) \\ x_1 + x_2 + x_3 & = 5, \end{align*}

which is impossible, as

\begin{equation*} 0 + 0 + 0 \neq 5. \end{equation*}