Chosen Solution
Hi, i replaced broken screen and battery in iPhone 5s but after that, phone is discharging really fast. I noticed, that it is discharging faster, when phone is locked (screen is off!). Time of discharging is about 10% per 10-20 minutes. Is it possible that battery is damaged (it was shipped to me with about 5 %)?
If your phone is running hot in a certain place then it has a short circuit somewhere resulting in decreased battery life. I was thinking you may have had a defective battery on hand as some vendors sell poor quality batteries but it sounds like that short circuit is the issue.