Answer
$2y(4x^2+y^2)(2x+y)(2x-y)$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $32x^4y-2y^5=\\=2y(16x^4-y^4)\\=2y((4x^2)^-(y^2)^2)\\=2y(4x^2+y^2)(4x^2-y^2)\\=2y(4x^2+y^2)((2x)^2-y^2)\\=2y(4x^2+y^2)(2x+y)(2x-y)$