Update to Lollipop (if you really want to - I wouldn't), then do a system cache wipe, don't do a factory reset. The only difference is that a factory reset wipes everything off the phone, which you're then going to reverse by putting everything back on the phone. You're doing something just to undo it - why bother?
It's not the factory reset that clears up the problems, it's the cache clear that's part of the factory reset that does - and you can do that from the Storage stats when the phone is running Lollipop. And remember, 5.0.1 is the bug fix for 5.0, and 5.0.2 is the bug fix for 5.0.1, so unless you're getting 5.0.2, you're knowingly putting buggy firmware into the phone. (I'm sure there will be a 5.0.3 to fix bugs in 5.0.2, but 5.0.2 hasn't totally bricked many phones.)