That's an impressive age for a rat. Mine usually last 2-3 years before something goes wrong. Strangely enough I've never had a rat develop tumors although that's fairly common. Mine usually slow down, seem to have mini-strokes and finally become so ataxic that I put them to sleep. Perhaps yours has developed some kind of heart problem. That behavior sounds like me (LOL)
Sadly, you rat is at the end of her life span. Five years is a grand old age for a rat. Does your rat have any obvious lumps that could possibly be tumors? Carcinoma's are very common in the rat. Or, is she losing balance as if she has an inner ear (equilibrium) problem, which could simply be a bacterial infection or something worse, like a brain tumor. It is very difficult to determine the cause of symptoms without more diagnostics, however. Can you take her to a vet? If not, please supply me with as much information as possible. Thanks!