The first integer is going to be x and the second one is going to be y.
We now turn the clues into equations:
x = y - 5
xy = 84
The substitution method:
(y - 5)y = 84
y^2 - 5y - 84 = 0
(y+7)(y-12) = 0
y = -7, 12.
If y = -7, then x = -12.
If y = 12, then x = 7