Priest in 5 Man Content

Hi! I'm a returning player; I've played Classic, TBC, and Cata, but nothing else.

I'd like to play Priest when TBC Anniversary comes out, but I only have experience healing in PvP, and that was ages ago. I'm planning to go Discipline for PvP content with a Mage friend. If I raid, I'd like to go as Shadow.

My question regards dungeon content while leveling; are 5 man dungeons going to be interested in a Shadow Priest, or should I expect to heal?