The x-coefficients have a nice ratio, and one of them is negative. That makes it easy to eliminate x by multiplying the first equation by 4 and adding the second equation:
4(5x+3y) +(-20x-7y) = 4(-10) +(15)
5y = -25 . . . . . simplify
y = -5 . . . . . . . divide by 5
Substitute this result into either equation to find x. I choose to use the first equation.
5x +3(-5) = -10
5x = 5 . . . . . . add 15
x = 1 . . . . . . . divide by 5
The solution is (x, y) = (1, -5).