I am having the exact same problem. I have had my phone for 9 months now and at first I was getting 5-6 hours SOT, but ever since I updated to Lollipop it has dropped significantly, 3-4 hours if Im lucky.
Also stuff like 'media server' and some google application thing seem to use a lot of juice.
I disabled Chrome (why can i not uninstall it??) as I thought it was the culprit as just browsing on it would rinse out the battery, but having installed Opera, it uses a similar amount, always the top battery user, even more than the screen. Is there any browser that doesn't use as much?
Anything else I can do?