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 :tongue:) mathematics that are not yet easily found in books. Any ideas mathematicians?