Exercise ( algebra )

Given that $$x^n-y^n = (x-y) (\sum_{k=1}^n x^{n-k}y^{k-1} )$$ with for example: $$x^4-y^4 = (x-y)(x^3 +x^2y +xy^2 + y^3)$$.
a) How would you factorize $x^5 + y^5$?
b) Generalize.
c) Prove the identity above for $x^n-y^n$ using mathematical induction.