To solve this equation, we can start by expanding the left side of the equation:

(x+5)(y-3) = xy - 3x + 5y - 15

Now we have the equation:

xy - 3x + 5y - 15 = 17

Next, let's move all the terms to one side of the equation:

xy - 3x + 5y - 15 - 17 = 0

xy - 3x + 5y - 32 = 0

Now, let's rearrange the terms:

xy + 5y - 3x - 32 = 0

Now, we can factor out the common terms:

y(x + 5) - 3(x + 5) = 0

Now, we can factor out (x + 5):

(x + 5)(y - 3) = 0

Now, we have two possible solutions:

x + 5 = 0 or y - 3 = 0

If x + 5 = 0, then x = -5

If y - 3 = 0, then y = 3

Therefore, the two possible solutions are (x, y) = (-5, 3)