"Closed" doesn't mean the apps are no longer running in the background. Few Android apps are truly shut down when you stop using them. Check the battery usage breakdown and see if there's a particular app that's using a lot of power. You can also start the phone in safe mode to keep much of the background stuff and programs you've added from loading at startup. (Turn the phone off. Turn the phone on, then hold the volume-down button until the phone finishes booing and says "safe mode" on the bottom left.) To get out of safe mode, restart the phone normally.
If safe mode doesn't extend your battery life, then it is what it is.
FWIW, I get much longer life from the S5 than I did with my Galaxy Nexus.