Does turning off wifi improve battery life?
Yes, turning off WiFi will save power.
In case you are not using any data it will but if you still gonna use cellular data with Wi-Fi off then it might be that you actually get less of battery life since data on cellular uses more battery than on WiFi especially if signal is weak.

For example for iPhone 6 (for 5 it was about the same) specs for Power and Battery are:

Internet use: Up to 10 hours on 3G, up to 10 hours on LTE, up to 11 hours on Wi‑Fi