Galaxy S5 Lollipop Lag - Possible issue with update?

For almost 6 months now my Samung Galaxy S5 has been running Android Lollipop 5.1.1 on T-Mobile, and every day I deal with a peculiar problem. It seems that the longer I keep my phone on, the slower it gets.

Every night I shut down my phone before going to bed, and every morning the problem seems to have reset. Early in the morning (after being off all night) my phone runs perfectly, with smooth animations and no issues with switching between and using multiple apps. Yet, as the day progresses, the phone begins to run more sluggishly. By the end of the night, using a single app like Snapchat with nothing else open in the background often causes freezing.

I've thought this could be an issue with the install arrising from updating OTA from 4.4.2 to 5.0 to 5.1.1, and I would have factory reset by now, except I can't bring myself to put myself through the headache of backing up data, reseting the phone, restoring data, and setting up everything again just for the possiblity that the problem will go away. Is there anyone else who has experienced this same issue? Can anyone offer any advice? Would a factory reset be worth it?