My mum's boyfriend's iphone 5s had terrible battery life. He had to buy a pocket charger just to keep it alive for his work day. It had to be fully charged at least 2-3 times a day and he would typically drain his pocket charger and still have his phone die in the early evening.
The repair did not go as well as it did when I replaced my own iphone 6 battery. One of the white adhesive strips under the old battery tore and was completely hidden under the battery. I did not have a heat source to attempt to melt it, so I had to pry the battery up on the side where the other adhesive strip had been successfully removed. I did eventually get the other adhesive strip off and the battery out. HOWEVER, I had only ordered the replacement battery for his phone, as I already had the tool kit from when I replaced my own battery. I did not realize that I would NOT receive the replacement adhesive strips, as when I ordered the full kit for myself the battery came with the strips. Thus, I was forced to improvise.
Make sure you order the replacement adhesive strips. And be super careful pulling out the old adhesive strips, don't let them tear enough to disappear under the battery.