Does turning off wifi improve battery life? I have an iPhone 5 with an unlimited data plan. I usually have it at home where I only have a mediocre cell signal. I don't want to put it in airplane mode just in case I get a call or text so would turning off wifi help save battery life even when I could be on wifi? I mainly use it just for communication if that helps. Thanks
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