Alright, so let's say that w = cis(72*)
Using demoivre's theorem, w^5 = 1
What I'm hung up on, now, is showing that w^4+w^3+w^2+w+1=0, I'm supposed to use something I already know about polynomials (synthetic division?), and knowing that both w and 1 are roots of f(x) = x^5 -1, but I'm drawing a total blank.
All help is very much appreciated.