To solve by elimination, you add or subtract the 2 equations to get rid of one of the variables. Since one equation has a 5x term and the other has a -5x term, if we add the two questions together, we can eliminate x.
-5x + 2y = 13
+ 5x + y = -1
The x terms drop out and you're left with:
2y + y = 13 + -1
3y = 12
y = 4
Now, you substitute y into either one of the original equations to get x.