Il Mio Problema
My 5S has been giving me battery problems for about 6-9 months and eventually I got tired of having to charge my phone almost every 2 hours. Sometimes my battery would drop suddenly (60 to 20% and other random disparities). My camera also stopped working around the same time due to "overheating" so I figure let's fix one problem (battery) and see if that fixes the other (camera).
La Mia Riparazione
The repair was testing and at times frustrating, but this was due to nerves, doubt and those stubborn adhesive strips. It took us about an hour to get it done but since this was our first time repairing an iPhone, I think that's very good. Be patient when trying to remove the adhesive and battery. Putting it back together is easy. Just ensure that you fasten back each circuit properly (this fixed my camera problem).
Il Mio Consiglio
The online instruction guides are very good but I recommend also using the video tutorials along the way. The pictures from the guide help but seeing someone else do it (video) gives you more confidence in carrying out each step. Both of the adhesive strips broke while we attempting to remove the battery and it was so frustrating! But you need to have A LOT of patience during the next few steps which involve heating the back of the phone to loosen the strips and using the spudger to remove the battery (we found that the flat end of it worked better than a card).