Welcome to the Apple Support Communities. If you are having issues with the battery life on your iPhone 5, there are a few things can be done to troubleshoot this issues. The first is to check your usage and standby time. If you look at it from your last full charge and your usage is higher than what you think it is, then you will be looking at some process on the phone that is running in the background. The next thing would be to restore the iPhone but do not restore from backup.
This article will assist in troubleshooting your iPhone.