x^5-y^5
=(x^3+y^3)(x^2-y^2)+x^3y^2-x^2y^3
=(x+y)(x^2-xy+y^2)(x+y)(x-y)+x^2y^2(x-y)
=(x-y)[(x+y)^2(x^2-xy+y^2)+x^2y^2]
=(x-y)[(x+y)(x^3+y^3)+x^2y^2)
=(x-y)[x^4+x^3y+x^2y^2+xy^3+y^4)