coefficient

We can use the binomial theorem, which is explained here --> https://www.mathsisfun.com/algebra/binomial-theorem.html
 

Since we're only finding the coefficient of y⁴, the exponent of the y is, well 4, while the exponent of the 7 is 1 (5-4). 

This means the y⁴ term is 5C1 * (2y)⁴-7¹

= 5(2y)⁴-7

 

= -35(2y)⁴

 

= -560y⁴

Which means the coefficient of y⁴ is -560, which is also your answer :)