\[\boxed{\text{1060\ (1060).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\left\{ \begin{matrix} x + xy + y = 5\ \ \ \\ y + yz + z = 11 \\ z + zx + x = 7\ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x + xy - yz - z = - 6 \\ y + yz - zx - x = 4\ \ \ \\ x + xy + y = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x(1 + y) - z(1 + y) = - 6 \\ y(1 + z) - x(1 + z) = 4\ \ \ \ \\ x(1 + y) + y = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} (x - z)(y + 1) = - 6 \\ (y - x)(1 + z) = 4\ \ \ \ \\ x = \frac{5 - y}{1 + y}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x_{1} = 1 \\ y_{1} = 2 \\ z_{1} = 3 \\ \end{matrix} \right.\ \text{\ \ \ \ }или\ \left\{ \begin{matrix} x_{2} = - 3 \\ y_{2} = - 4\ \\ z_{2} = - 5. \\ \end{matrix} \right.\ \]
\[Ответ:(1;2;3)\ \ или\ \ \]
\[( - 3;\ - 4;\ - 5).\]