I called Apple Support and convinced them to give me a replacement iPhone5. They were willing to do so because I have an Apple Care Plus plan in place on my iPhone5. The battery on the new replacement iPhone5 lasts a lot longer. Plus I have implemented some of the things that Apple recommends on it's iPhone Battery page, and now my new replacement iPhone5 lasts all day and evening on a single charge. I turned off location services for everything except Find My Phone and Camera. I turn it on selectively for other apps and turn it off when I am finished using that app. I also turned off Alerts for everything except Calendar, Phone and Reminders. And I turned off Badge App Icons for everything except Messages and App Store. And I turned my screen brightness down to 75% of max. I did not implement the rest of Apple's battery saving recommendations because to do so would essentially make your iPhone5 not useable for much of anything. Those three changes, plus a new replacement iPhone5, solved the problem for me.
Here is a link to the Battery info provided by Apple:
http://www.apple.com/batteries/iphone.html