Can 5th order equations be solved by means other than radicals?

[meldraft]

As the title suggests, we know from the Abel-Rufini theorem that 5th order equations cannot be solved using radicals. I haven't managed however to find an either positive or negative answer to the following statement:

"Can 5th order equations be analytically solved by means other than radicals?"

This of course rules out numerical solutions. It is pretty contrary to my intuition, however I am entertaining the notion in case it can be solved using modern (or exotic ) mathematics that are not yet easily found in books.

Any ideas mathematicians?

 

[Stephen Tashi]

In a history of math book that I read as a teenager, I recall that Hermite produced a non-algebraic solution. So I just now went searching for it on the web, and I think it is this:
http://en.wikipedia.org/wiki/Bring_radical See the section on The Hermite–Kronecker–Brioschi characterization. I haven't studied this material.