By the Binomial Theorem,
[(2y-5)^6 = \binom{6}{0}(2y)^6(-5)^0 + \binom{6}{1}(2y)^5(-5)^1 + \binom{6}{2}(2y)^4(-5)^2 + \binom{6}{3}(2y)^3(-5)^3 + \binom{6}{4}(2y)^2(-5)^4 + \binom{6}{5}(2y)^1(-5)^5 + \binom{6}{6}(2y)^0(-5)^6.]
The coefficient of y4 is \(\binom{6}{4} (2y)^2 (-5)^2 = \boxed{480}\).
