5x - 9y =  7      
7y - 3x = -5      


First, write it in the standard form


 5x - 9y =  7        (1)
-3x + 7y = -5.       (2)


Apply the Elimination method.


For it, multiply equation  (2)  by 3  (both sides); then multiply equation (2) by 5 (both sides). 
You will get an equivalent system


 15x - 27y =  21     (3)
-15x + 35y = -25.    (4)


Now add equations (3) and (4).  The x-terms will cancel each other, and  you will get a single equation for unknown y only:


 -27y + 35y = 21 + (-25)

   8y = -4  

    y =  = -0.5.


Now from equation (1),  5x = 7 + 9y = 7 + 9*(-0.5) = 7 - 4.5 = 2.5  ====>  x =  = 0.5.


Answer.  x= 0.5;  y= -0.5.


Check.   Check the solution on your own by substituting into equations (1) and (2).