Hi Sarah. Babies tend to come out of their deep sleep cycle around 4 in the morning for some reason. This could be what is happening with your LO. Is she taking a full feed at 5 am? Or does it seem like more of a snack? Is she settling back into sleep after she eats? Is she bottle or breast fed? If breast fed, then that does seem an awfully long time between her DF and her morning feed.
IMO, if she is taking a full feed, she must be hungry. If she's just taking a snack then it's just her coming out of her sleep cycle. I'd give her a few minutes to resettle herself without your intervention. If need be, go in to her and put your hand on her. She may fall back asleep fairly quickly.
HTH!!