Well. It's been about a week since I've been rockin my new iPhone 5 with 0 problems. Worked with Apple support to confirm it was a battery failure issue and not an iOS issue. Opted for rapid replacement and had my phone within 3 days. After receiving the phone, I just sent my iPhone with the defective battery back to them in the same package with a prepaid label. Pretty painless experience. If you're still under warranty, check with Apple Support regarding your specific issue.
I had this same battery problem and I instantly noticed it after installing two apps by Onavo, the data counter and compressor. Has anyone had this issue? I deleted the apps and removed the Onavo account from the VPN but the battery is still charging slower and draining quicker. I was so impressed with how quickly it charged and how long it lasted when I went from iPhone 4 to 5s. That was with all the bells and whistles being on, now it's really bad. Could Onavo still be affecting battery performance?