Willie -
You can approach this two ways: (1) substitution or (2) elimination. I recommend substitution since y is easy to isolate in the first equation:
2x - y = 5, so solving for y:
y = 2x - 5
So, here is where the substitution comes in ... wherever you see a "y" in the second equation, simply substitute (2x - 5), then solve for x:
5x - 2y = = 8
5x - 2(2x - 5) = 8
5x -4x +10 = 8
x = -2
Now, simply use x = -2 in any of the two original equations to solve for y.
I'll leave the math for you!
Hope that helps :)