The easy way to solve this problem is to plug the coordinates (ordered pair) into your system of equations. Remember that ordered pairs are expressed in the form (x,y) so our equations should be rewritten as follows:
2/3(5)+5(-5)=56
7(5)-8/5(-5)= 47
We'll now simplify the first equation:
3 1/3 + (-25) = 56
3 1/3 - 25 = 56
-21 2/3 = 56
This is obviously untrue, meaning the ordered (5,-5) doesn't solve the first equation. We can stop here, but lets check the second equation for fun:
35 - (-8)= 47
35+8=47
43=47
again this is false so the (5,-5) isn't a solution to the system of equations, or even either one of the equations.