jmc

Multiplying the first equation by 5 and the second equation by $-2$ gives $$\begin{array}{rl}10x-15y& =-25,\\ -10x+4y& =-8.\end{array}$$Adding the two equations gives $-11y=-33$, so $y=3$. Substituting $y=3$ in the first original equation gives $2x-9=-5$, so $2x=4$ and $x=2$. Therefore, the solution is $(x,y)=\boxed{(2,3)}$.