I think you would have a better shot at getting five, two-champ teams, as in 2 v 2 v 2 v 2 v 2. Or four, three-champ teams 3 v 3 v 3 v 3. Your problem with teams of 5 is that you would end up with too many connection issues, or as Judge Arcadia said, some toasters simply couldn't handle it. Riot is making an effort to make their games easier to run on the average machine so I don't see them going to that extreme. Safest to keep the number of players to 'about' the same number as SR.
Also, working with smaller teams would make diversity in game play and strategy more interesting in my opinion. having teams of 2 would most likely end up with either a carry (AP or AD) and a support, or carry/tank, tank/support, .. I'd say it wouldn't be likely for the 2 champ teams to support many junglers
3 champ teams could have more diversity, including the chance for jungelers.
Which actually brings us to the map itself.
I don't see it really working out on summoner's rift specifically. They would need a map with more manageable lanes, shorter, narrower, or at least less spread apart. There would also have to be pathways to each base that would take equal effort to siege and defend. This could be a problem if there are 5 teams because someone would most likely be out-flanked or ignored.
However, this is also assuming that the game type is the same siege style as we are used to on SR. This layout could open up different game types too. King of the Hill?
Central territory that must be captured and held against enemies for a certain length of time (A lot like Crystal Scar, but one territory)
Capture the 'flag'?
Central 'flag' I'm thinking maybe something more like a Poro King (large, slow-moving, neutral monster with a lot of health) which must be persuaded and guarded to the team base before being killed by the enemy teams.
Team Deathmatch?
Time limit or Kill Cap game of pure mayhem.
Just to name a few
** After having typed all of this out, I think I am going to copy at least my game type portion and make a new thread. **