x, y - two positive integers
product of two positive integers is 120
(1) xy = 120
one number is 2 less than five times the other
(2) x = 5y -2 substitute it to (1)
(5y - 2)y = 120 use distributive property
(5y)(y) - (2)(y) = 120
5y² - 2y = 120 subtract 120 from both sides
5y² - 2y - 120 = 0
use quadratic formula
a = 5, b = -2, c = -120
b² - 4ac = (-2)^2 - 4(5)(-120) = 4 + 2400 = 2404
√2404 is irrational number, therefore
Answer: no solution in integer numbers