Help would be appreciated

Find the coefficient of y^4 in the expansion of (2y - 5)^7. 

The general term in the expansion will be

$\binom{7}{n}(-5)^n(2y)^{7-n}$

if I rearrange  this I get

$\binom{7}{n}(-5)^n(2)^{7-n}(y)^{7-n}\\ $

you want y^4

so  7-n=4    gives     n=3

sub n=3 into the term and you will have your answer

$\binom{7}{n}(-5)^n(2)^{7-n}(y)^{7-n}\\ n=3\\ \binom{7}{3}(-5)^3(2)^{7-3}(y)^{7-3}\\ $

You can finish it.