During RAF, I leveled a whole bunch of 5x the Same Class.

I've leveled 5x Feral Druids to 85th.
You could easily do most 5-man content, as the Druid class gets you Tank + Healer + 3x DPS.
During the leveling up, they were always able to successfully take down a +1 level elite, without the quest item to make the mob weaker; the only one they didn't get was the guy that pulses in Hyjal and you have to run out from his fire; definitely way stronger in what they could take out while leveling up, than my latest team of 4x DK's and a Paladin.
I think the 4x DK's and Paladin will be a stronger team when geared; plus Blizzard seems to buff DK's every patch, and nerf Druids... which is a bonus for the DK team.

I'm also slowly leveling 5x Paladins.
Running these as Exorcism/Shockadins, with the intention of stopping experience at 72nd (Avenging Wrath) for play as twinks in the 70-74 bracket.
Paladins get you a Tank (Prot), Healer (Holy) and DPS (Ret), so you could likely run a lot of 5-man content with an all Pally team too.

I like 5x Priests (mine are all Disc).
I don't see them going far in Heroics, without a tank.
But they're fun, and I would imagine with some gearing they would be rather sick to go against in PvP.
Adding any tank to the group, should open most 5-man content.

I leveled the DK's together.
Have since moved one of them to join a mixed team, as the PvE Heroic team.
But 5x Blood Spec DK's, could run a lot of 5-man content.
You have Rune Tap, every 30 seconds... which heals 25% of your maximum health across the entire team.
Combine that with round-robin taunt, to spread the pain about.
Blood worms from lots of toons, healing everyone.
And Death Strike which glyphed will heal a minimum of 15% of your maximum health.
I could see 5x DK's doing most non-heroic instances.

I have a lower level team that hasn't been touched in a while.
4x Warlocks and a Priest.
I could see 5x Warlocks as being a successful team for PvP.
And likely able to do all non-heroic 5-man content, at least up to early WotLK.
Heroics would not be possible, or I doubt it anyway.

My 5x Hunters rock in PvE (outdoors).
But they're 75th, and not likely to progress until Alchemy requires higher than 75 (next expansion) for maximum skill cap and the new transmutes.