Super Bomberman only allowed you to play with 4 players, though I think Super Bomberman 2 may have allowed 5...I don't think it did.
The only games I know for sure that allowed 5 were the EA sports games. But, those games weren't good with 5 players. It is actually quite silly to play sports games with more than 2 people.
But 5 players is crazy, because it means one time always has that 3rd human player advantage, that would just suck.
I also think that perhaps the Micromachine game/games for SNES allowed 5 players as well.