My daughters phone started lasting somewhere into the ballpark of 40 or so minutes after first updating to 10.1.1. Then I upgraded her to the 10.2..... and the phone lasted less than 20 minutes.
Update:
A friend gave us a broken 5S which luckily I was able to have repaired for a decent price so I migrated my daughter to the newer phone. We avoided installing from a backup. I just redid her phone one bit at a time. Now everything is nice and tidy and the install is clean. Her 5S is working pretty well although it too seems to be draining more quickly than my own 5S. At least it doesn't spontaneously shut itself off at 35% or 50-70% as her iPhone5 was doing.
With her old battery drain & shutdown iPhone 5, I did a factory re-install in recovery mode.
Now the phone has lasted about 3 hours and it is down to 19 minutes sitting in standby mode. Before the upgrades it would last all day and overnight. I miss that longevity. Still 3+ hours is better and I am not done tinkering just yet.
I will leave it overnight until it dies and then plug it in to see if it charges fully. I will let it charge until tomorrow evening and see if I can induce the iPhone 5 to last a bit longer.
At least it is not spontaneously shutting itself down right now.
Perhaps I can re-calibrate the battery which I have heard some people talk about.
Perhaps the battery is damaged or diminished at this point from all of the perpetual shutdowns and recharges.
Regardless, I need to check whether the phone can be redeemed back to its former self from a month ago.
If it continues to misbehave, I may take it to the Bulb & Battery store which will replace the Battery for about 50 bucks.
Maybe then the phone will finally behave more like new.