How do I close apps on IPhone 5s?

Double tap the Home button, then swipe upwards on the Preview of the App(s) you wish to close.

Tap the Home button when done.

Note that, unless the app is doing something is shouldn't, there's no reason to force close an app. Most of the apps that you see when you're performing the above procedure are not doing anything.

See this article for more information:

https://support.apple.com/en-us/HT202070

If your concern is battery life, go to Settings>General>Background App Refresh and turn it off for all the apps for which you don't need it. Or, turn it off completely.