After every major update I do an FDR, even the smaller updates.
For example, I had my 2012 Wifi Nexus 7 running on 5.0.1. I had updated it to 5.1 as soon as it became available and my device was brought to a crawl in terms of performance. Opening any app was a pain and even running Clean Master before use had become part of the routine after booting it up.
I don't use my Nexus 7 as much as I used to so I decided to just do an FDR as there isn't anything important on it. The difference after was night and day, it runs smooth, apps open quickly, and I don't even have Clean Master installed on it anymore.
Yes doing an FDR is a pain, but it's the suggested remedy for a reason. New OS (well at least updated), so why not start on a clean slate? @leeshor gave you great advice and you could try to narrow it down if you want, but if Android System is the culprit then an FDR should get your battery life back to where it used to be.
If you have any concerns about backups you can use these to help save what you want:
Photos - Google+ backup (or your SD card)
SMS/MMS - SMS Backup & Restore (save file can be emailed or to your SD card)
Any other apps you have that need info to be save (such as aCar, which I use), they can be backed up to in their programs and usually be exported to another source such as email or SD card.
I would do as @leeshor states and check your usage before jumping into an FDR if that's your concern. You also got to take notice of your own usage too (i.e. playing games, refreshing emails a lot, account settings, brightness etc.). I would also after you do your day of usage on that monitor post a screenshot of Settings > Battery graph. I have a completely different phone than you though (Nexus 6) and my battery is alright if I don't catch myself on a binge of Game of Thrones by Telltale or Knights of the Old Republic. Basically, rule out anything logically that you know would cause a battery drain before jumping into an FDR. Leave it as a last resort is kind of what I do when I troubleshoot any issue.
Well, I do have kind of a nice Tech support background that helps in some situations. I've worked for Apple for a little over 3 years now. Let me tell you, that training did help me hone some of my troubleshooting for Android devices. For example, the FDR you're concerned about, Apple calls it a restore. We use it as a last resort because it will erase customer data and if they don't have a backup...well that's now a very angry customer.
It doesn't look to mew like you have a serious problem. It says 9.5 hrs. use with 48% left. I certainly don't see the need for the FDR but you may consider turning off auto brightness if it's on and maually adj the screen down a little. If it was me I would also put WeatherBug on a manual refresh, but that's me.
Quite honestly, I feel my battery drains much faster since Lollipop. I don't remember my phone dropping 5% in battery making a 10 minute phone call before...which it did this morning. Maybe I'm wrong, but I think I am going to do a FDR anyway. I've had the phone for a year....I see FDR as a "refresh" for hoping the next year, which at that point I'll probably be ready to upgrade to the next Note.
I don't see a reason to do the FDR. It looks like you use your phone a lot and have your screen a tad brighter than you might otherwise have it but if you continue to use it for the same things a reset will only benefit you for short time before you will see the same usage.