I can get my head around this so someone explain it please.
$(1)$ From Galois theory it is known there is no formula to solve a general quintic equation.
But it is known a general quintic can be solved for the 5 roots exactly. Back in 1858 Hermite and Kronecker independently showed the quintic can be exactly solved for (using elliptic modular function). Also I think they're maybe other solution for the quintic which means a formula for each of the 5 roots.
So why is the claim in Galois theory that there is no formula to solve it? I know I am missing something here because the above $(1)$ is an established result.
So what is the value in saying, using Galois theory we do not have a formula for the 5 roots? Since for practical purposes we can actually find the 5 roots each time using say for example the formula based on elliptic modular functions.