To solve this system of equations, we can use the method of substitution or elimination.

Let's use the method of substitution.

From the first equation, we can solve for x in terms of y:
2x + 3y = 5
2x = 5 - 3y
x = (5 - 3y) / 2

Now, substitute x into the second equation:
-(5 - 3y) / 2 + 2y = 5
-5 + 3y + 4y = 10
7y = 15
y = 15 / 7

Now, substitute y back into the equation to solve for x:
x = (5 - 3(15/7)) / 2
x = (5 - 45/7) / 2
x = (35/7 - 45/7) / 2
x = -10/7

Therefore, the solution to the system of equations is x = -10/7 and y = 15/7.