I have a few suggestions for you. The book Healthy Sleep Habits, Happy Child by Marc Weissbluth is a great sleep resource on many of your questions, and I like most of his methods (some are a bit too baby-unfriendly for me, but most are very nice). I would definitely recommend getting this book, as he talks a lot about how much sleep babies need at different ages, and you will be able to see that yours (as I'm sure you expect) is not getting enough sleep.
Next, I'd try to push that morning nap back until a bit later. I find that my dd starts getting up earlier in the morning if I move her nap up (she's also been sick recently and so has been waking earlier, napping earlier, and all of a sudden she's up at 5 this a.m.!) Try moving the nap back in 15 min increments each day until its 30 or 45 min later and see if that helps.
I have also read that if you put your child down when they're over-tired, they actually won't sleep as long into the morning. I don't know whether I've personally found this to be true, but when you're in a bad sleep pattern, as you are, I would try anything! My dd at 11 mo was getting up early every day and I tried it all!!
Finally, what did actually work for me in getting rid of the early a.m. wakings was getting up exactly 1 to 2 hrs before she would normally get up (so if yours wakes at 5, go in between 3 and 4), gently resettling baby (shifting blanket, etc. - enough so you know you've broken they're sleep pattern but not necessarily totally waking them up), and after 3 nights, wait a few days and see if this gets better. This "Wake to Sleep" method is in one of Tracy's books, but I'm not sure which.
Good luck! I know how miserable it can be, but stick with it. It will get better.