iPhone 5s using too much data on Wi-Fi
EDIT: Below is my original answer (for posterity). It describes turning off "Wi-Fi Assist" which, while reducing cellular data use, DOES NOT answer OP's question of reducing data use. For Apple's built-in solution to reduce data usage on cellular, see my other answer.

Go to settings -> cellular. Scroll down past the list of apps to "Wi-Fi Assist" and turn it off! This has been a huge problem for lots of people. Wifi Assist is turned on by default. When it's on, whenever your mobile data is faster than your wifi, it uses your mobile data without telling you.
Your problem should disappear after you've completed this step.