M.E.
I hate to say it, but you might want to let her cry it out until the 5am feeding. Kids need to learn how to self soothe, and since your used to know how, you're going to have to let her figure it out again. Believe me I know how emotionally distressing it is to hear your little one cry! However, since you know she used to be able to sleep that long, and she's getting enough to eat, try letting her cry for 10-15 mins. Then, if she hasn't gone back to sleep, go in and rub her back/belly until she calms down, kiss her goodnight again, and leave her.
My daughter also started having gum pain around 3-4 months, but it only affected her falling asleep. She'll let you know if its her gums by biting your hand. I use baby orajel at night on her gums to get her to sleep.
We also have the problem about getting up at 5am. I can't break that either. She goes down at between 8 and 9 and won't sleep past 5! Even now that she's eating solids. Fortunately that's what time my husband gets up for work anyway, but she's wide awake then and happy (unlike her parents!) She gets fed, then it's 50/50 whether she'll go back to sleep again, or wait for her next nap. It might be normal for your daughter too!