Apparently my iPhone 5 is a part of a batch of units that has a flawed battery straight from the manufacturer.
Fortunately after contacting Apple online, verifying my serial number online, verifying my failed battery via over-the-phone diagnostic I was found eligible to receive a replacement battery free of charge ($79 value). I made a service appointment with the Apple Store at Fashion Show Mall online. I arrived very late, but was still able to be seen and serviced. I waited for about 25 minutes, then was seen by an Apple employee. He asked me what was going on with my phone, verified my serial number, ran a diagnostic and took the phone to the back for repair. Thirty more minutes passed, and the phone's battery was replaced. It has been a week, and the battery is performing substantially better than before. Excellent customer service and excellent repair made this visit satisfactory.