Normally I scan all my receipts, but I can't seem to find this one.
I would say that it's at the tail end of that 5 years and I've never changed the battery. If it would come to ordering a battery for it, I don't know as though I would stick with Cyberpower because I've since heard some bad reviews on them.
I have no idea what the last questions is about. All I know is that the PSU that I installed in my pc build is a Corsair RM650x. Never heard the term PFC before.
Edit : Just found out what PFC stands for and no, my current UPS is not a PFC unit.
5 years that battery is toast. They generally last more like 3 tops.
I have 3 Cyberpower units in service in my home right now all work very well, however one of them I did replace the battery on, but it never had the issues you are having.
Your PSU Corsair RM650x is ActivePFC, the short version of a long story is it tends to be sensitive to the power changeover in a UPS between battery and wall power. That could have something to do with your issue if its a cheaper Cyberpower unit, but the battery is clearly dead, and on top of that it shouldn't be switching randomly.
IMO replace the whole unit. Make sure you get one thats 1000va at a minimum due to the size of your PSU you want to make sure your UPS can handle it at max draw if you were to use a high powered GPU. And one that can handle Active PFC.