>>12813006>This isn't really an answer, it's just restatingI understand that it's not a super satisfactory answer, but 4chan is not the place to tell you the intricacies of Galois theory. That shit requires 2 semesters of undergrad abstract algebra to begin to understand. However, to sum it up the unsolvability of quintics in radicals rely on the fact that the alternating groups A5 and up are simple. You can look up the proof of simplicity of the alternating groups. It has nothing to do with Galois theory and is an independent result.