Step 1 :Multiply the first equation by 5 and the second equation by 1 to get two new equations: 5x + 25y = -75 and 5x + 3y = 13.
Step 2 :Subtract the second equation from the first to eliminate y: 22y = -88.
Step 3 :Divide both sides of the equation by 22 to solve for y: y = -4.
Step 4 :Substitute y = -4 into the first original equation to solve for x: x + 5*(-4) = -15, which simplifies to x = 5.
Step 5 :The solution to the system of equations is \(\boxed{(5, -4)}\).