Question 661573
x-y=5
xy=204
Substitution
(5+y)y=204
5y +y^2-204=0
Rearrange
y^2 + 5y - 204 = 0
(y+  )(y-  ) mixed sign due to - 204
Multiples of 204 that will subtract to equal 5:  12,17
(y + 17 )(y - 12 )
y+17=0, so y = -17 NO, must be positive integer
y-12=0, so y = 12 Yes!
x-12=5, so x=5+12=17
Proof
17-12 = 5
17*12 = 204