LHIRT POD #4

About time I wrote another of these. This one is not mine, and it's not particularly difficult, but I liked it because it elucidated in my own head some properties about roots:

Let x_i be the roots of the equation x⁵+2x+5=0. What is the sum of all x_i⁵, without jumping to Mathematica for the answer?

I have another one, but I'm tinkering with this new operation I've been looking at that is commutative, not associative, nilpotent, and has some cool closure properties, and wanted to first come up with a problem that uses that operator. I guess the proper term for this algebra is a nilpotent loop, and it has some really interesting math behind it (not to mention some intriguing open problems in that algebra and some sibling algebras).