Question 774959
Let the numbers be 'x' and 'y'.
Let the larger number be 'x'.
So    x = y + 5 -----------------(1)
Also  xy = 84 -------------------(2)
Putting the value of 'x' from equation 1 in equation 2 we get
      (y + 5)y = 84
or    y^2 + 5y = 84
or    y^2 + 5y - 84 = 0
or    y^2 - 7y + 12y - 84 = 0
or    y(y-7) + 12(y-7) = 0
or    (y - 7)(y + 12) = 0
or    y = 7 or -12

So    x = y + 5 = 7 + 5 = 12 
               or
      x = y + 5 = -12 + 5 = -7

Therefore the two numbers are either (12,7) or (-7,-12)

check:    xy = 84
      Putting the two sets of values in the above equation we have
      i)   12*7 = 84
      ii) (-7)*(-12) = 84