We’ve seen some complaints surfacing lately about the battery life of the iPhone 5(s), and how it may not be that great.
While a bad battery can cause some significant issues (and can be easily replaced), the vast majority of problems can be fixed by addressing battery-draining, software-related issues first.
For a great step-by-step on things to check, have a look here:
http://www.payetteforward.com/why-does-my-iphone-battery-die-so-fast-heres-the-real-fix/