expand (a - b)^n. We get,
a^n*(1 + (-b/a))^n = a^n{1 + n(-b/a) + n(n-1)(-b/a)^2/2 + n(n-1)(n-2)(-b /a)^3/3! + n(n-1)(n-2)(n-3)(-b /a)^4/4! + n(n-1)(n-2)(n-3)(n-4)(-b /a)^5/5! + ... }
The sum of the 5th and 6th terns is zero, so then
n(n-1)(n-2)(n-3)(-b /a)^4/4! + n(n-1)(n-2)(n-3)(n-4)(-b /a)^5/5! = 0
Cancelling out common factors,
(-b /a)^4/4! + (n-4)(-b /a)^5/5! = 0
Cancelling out more common factors,
1/4! + (n-4)(-b /a)/5! = 0
1 + (n-4)(-b/a)/5 = 0
5 = (n-4)(b/a)
(a/b) = (n-4)/5, n ≥5