5 hrs screen time is a lot for any phone. I'm a moderate to heavy user and I might see 4 hrs screen time in a day occasionally. A lot more talk time but screen trumps talk in battery use. And touch the battery graph to see your signal and awake time. Might be something there.
ATT N3
Talk uses about as much battery in my experience
Sent from my Galaxy S4 running SlimKat 4.4.2