There's nothing more annoying than watching your iPhone go from lasting a whole day on a charge to dying in just a couple of hours. In most cases, battery drain is caused by a hardware intensive app being left on in the background or data being refreshed while your phone is sleeping.
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A rapid drain on your iPhone 5S's battery can be caused by a runaway app or process. Rather than trying to track down which one it is, it's far easier just to reboot your phone. It is worth noting, however, that some apps are more power hungry than others, and they will continue to eat your battery life while running in the background. Navigation apps or anything else that uses the phone's GPS transceiver, streaming audio and video apps, and VoIP apps, like Skype, can consume massive amounts of power. Close these when they are not in use by double-clicking the Home button, then using your finger to "flick" them up off the screen.
By default, the iPhone will refresh apps and download updates in the background, even while you're not using your phone. This can be disabled under "Settings," "General," "Background App Refresh." Push notifications can also cause battery drain, so disable notifications from apps you aren't concerned about by going to "Settings" and "Notifications." Finally, disabling Location Services under "Settings," "Privacy" will keep the GPS unit in your phone from running constantly, draining your battery.