I've also had this problem, and so has my boyfriend's iPhone 5. He's had his phone checked at an Apple Store and the battery diagnostic said his battery was still fine. I have noticed this problem only started occurring after iOS 7 so I think it's a software problem rather than a hardware problem.
I've had my iPhone 5 for about a year and have been noticing the same problem. I find it's worse when it's cold outside.
My wife has constant battery life issues with her iPhone 5. I don't know if she has the one you mention, Dave, but she'll frequently see her battery life drop extremely quickly. She'll see 70% at some point, then around 20 minutes later it'll be at 50% or lower. We have no idea why this happens.
I´ve had the same issue with my iPhone 5 battery ever since I updated to iOS 7. Do you know if there is any way to revert back to iOS 6?? It lasted longer then, and now it not only goes from 90% to 50% in minutes, it shuts off somewhere between 35% and 20%. It is a pain, I´ve researched ways to preserve battery and I continuously do all that I can, like closing apps, turning off wifi when Im not around useful wifi, turned off blue tooth, parallax and other features... but the battery still drains and my phone spends most of the day plugged to a charger. It sucks! iOS 7 sucks too in my opinion! I am a mac person, but lately I find myself drooling over my best friend´s Samsung Galaxy S4 Note. Her battery lasts forever and I envy the huge screen and the notepad... Maybe I should just change it!
Do you have any updates on this issue since you wrote this?
Is Apple doing something about this issue on so many iPhones 5??