A different proof of the insolubility of the quintic?

This is the content of the Abel-Ruffini theorem (whose proof predates Galois')

http://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem

A topological proof may be found in this paper.

https://www.tmna.ncu.pl/static/files/v16n2-02.pdf