Sadly I have come to find the same as you did... 5 Shamans just dont do it anymore once you dinged 80 with them. Anyways your are not supposed to just walk into heroics with quest-rewards and wipe the floor there. You seriously need to have a "meatshield" in place with the last patch. The issue is that Eart Elementals and Fire Elementals didnt get a new Rank since 70 and atm they scale just horribly. I expect some changes to these spells in upcoming patches which then hopefully make it possible again to clear heroics with just shamans... but for the time being you should seriously consider getting a tank. I heard Death Knights seem to be useful.. looks like im gonna try leveling one.
The thing is I havent really tried intensively cleaning non-heroic instances so far (except Statholme, where the 1st boss already gave me a headache) but the first boss in Utgarde Pinnacle (on heroic) on-hit my Shaman!!!!!!!! the other day and I dont see that changing with "high-level" reputation epics from the different factions. Only thing to do I think, get your healing macros in place and level up a Tank.