\[x + y = 13 \Longrightarrow \ \ \ y = - x + 13\]
\[\ - x + 13 = - x^{2} + 5x + 5,\ \ \]
\[x^{2} - 6x + 8 = 0\]
\[x_{1} + x_{2} = 6\ \ \ \ \ \ \ \ \ \ x_{1} = 2\]
\[x_{1} \cdot x_{2} = 8\ \ \ \ \ \ \ \ \ \ \ \ x_{2} = 4\]
\[y_{1} = - 2 + 13 = 11\]
\[y_{2} = - 4 + 13 = 9\]
\[Ответ:(2;\ 11);\ \ (4;9).\]