Please ignore Shodokan. He's not an "out of the box" thinker.

A priest and four warlocks CAN do dungeons, at least in the 0-60 range. Just got to be creative. A guildie of mine just did 1-70 with 5x Priests (disc I think?) and knocked out every dungeon along the way as far as I know.

As far as wrath dungeons - you can probably do some of them, but its going to be hard. And heroics are probably a no go altogether because pets may get insta-gibbed.

I'm thinking a Disc priest for OP shields and "oh shit" buttons to keep the pets up.