Answer
$\left( \dfrac{7}{3},-\dfrac{8}{3} \right)$
Work Step by Step
Substituting $y=x-5$ in the second equation results to
\begin{array}{l}\require{cancel}
y=-2x+2
\\\\
x-5=-2x+2
\\\\
x+2x=2+5
\\\\
3x=7
\\\\
x=\dfrac{7}{3}
.\end{array}
Substituting $x=\dfrac{7}{3}$ into the first equation results to
\begin{array}{l}\require{cancel}
y=x-5
\\\\
y=\dfrac{7}{3}-5
\\\\
y=\dfrac{7}{3}-\dfrac{15}{3}
\\\\
y=-\dfrac{8}{3}
.\end{array}
Hence, the solution set is $
\left( \dfrac{7}{3},-\dfrac{8}{3} \right)
.$