Are you looking for the possible values of x and y?
In that case, let's factor it!
xy + 5y + 4x + 20 = 1
y ( x + 5 ) + 4 ( x + 5 ) = 1
( y + 4 ) ( x + 5 ) = 1
Since 1 can ony be represented as 1 * 1 or (-1) * (-1), the only "friendly" integer solutions I see are...
x = -6, y = -5 (-6, -5)
x = -4, y = -3 (-4, -3)