iphone 5's did that starting with ios 7, like thousands of them, maybe even millions. the apple store here was flooded with line ups of people complaining of the same thing on the same device, batch of defective batteries alright..you can only tell if its a bug if going back to 7.1.2 clearly fixes it by shutting down at 1 or 2%. i insisted for a long time it was ios 7's fault but a replaced battery did fix it, & 8 months later, its still normal, dying at 1%.
one time in the winter i fully charged the battery 100% before i left, by the time i got to my bus stop 15 mins later, with the phone in my sleeve + hand around it so its moderately slightly warm, it shut down & gave me low battery icon, took about 20 tries then it booted, & said 100%...was beyond pissed. i still have the lowbatterylog from that as well, the apple genius was speechless when i showed him it & 10 mins later said it failed 100% of diags
look at those awake/standby times
partial charge shows i did a full charge
the capacity it "died" at