It's not 'abnormal'.
http://www.apple.com/batteries/iphone.html
iPhone 5s and iPhone 5c offer up to 10 hours of talk time on 3G, 8 hours of Internet use on 3G, 10 hours of Internet use on Wi-Fi, 10 hours of video playback, or 40 hours of audio playback on a full charge at original capacity. In addition, iPhone 5s and iPhone 5c feature up to 250 hours of standby time.
Try this controlled test:
- First, charge up the device to 100%. To enable the percentage indicator, go to Settings > General > Usage, and turn on Battery Percentage.
- Once the device is charged to 100%, make sure to close out all Apps that are running on the device. In iOS 7, you close out running apps by double-tapping the Home Button, and then swiping your finger up across the preview screen of each app to move it off the top of the screen.
- Then, turn off wi-fi and cellular data. Settings > Wi-Fi > Wi-Fi: OFF & Settings > Cellular > Cellular Data: OFF. This will not prevent you from receiving any phone calls, although it will prevent text messages. If you want to still be able to get text messages overnight, leave Cellular Data ON.
- Go back to the Home Screen, and take a screenshot. Press both the Sleep/Wake button and the Home button together briefly, and you will see the screen flash white for a split-second, and an image will be saved to your Photo App Camera Roll.
- Disconnect the iPhone from the charger, and lock the screen so it is dark.
- Let the iPhone sit in this ‘standby state’ for as long as possible, preferably overnight.
- In the morning, unlock the screen, and then take a screenshot of the Home Screen again.