Hi K.,
I can relate. I have 6 kids who all share rooms, and we have had plenty of sleep issues. The book that saved our lives was "Healthy Sleep Habits, Happy Child," by Dr. Marc Weissbluth. It was recommended to us by our pediatrician when we were in a time of absolute desperation with our fourth baby. The book breaks things down by ages, and walks you through step by step. It usually, in my experience takes only a few days to resolve most of the sleep issues. We've used it so many times with various kids at various ages. It would probably have you start with the daytime sleep, and once that's under control, the night. But also, considering that your daughter is not sleeping much during the day with her 5:30 wake-up, you could try napping her a little earlier in the day, and putting her to bed by 6pm. I know this seems ridiculously early, but an earlier bedtime often seems to actually improve both quality and duration of nighttime sleep. I would never have thought of doing that, but when I tried it, it worked. Also, letting her cry it out is part of this method, and is awful the first couple of nights, but you'd be amazed how quickly it ends after that. With a couple of mine, I had to take my older child out of the room for a few nights, so it wouldn't disrupt her sleep, but I found that was worth it. Also, my kids usually have managed to sleep through the crying any time I've had to use this method. I would definitely recommend getting the book though, because there is a lot more to the process than I could possibly ever explain, and he also explains away very satisfactorily, most of the arguments against letting a baby cry it out, especially one as old as your daughter. Good luck.