Just successfully changed my iphone 5 battery! I read all the comments beforehand and used the guitar pick method to get the phone open initially. I used the plastic tool to pry by the headphone jack while my sister shoved a guitar pick on the opposite side while I pulled the suction cup. That was the hardest part.

Then, I went ahead and did not disconnect the screen since my sister was helping and could just hold it open. It was tough to get the battery out and the old one got kind of warped, but it wasn't working anyway. After that, just plopped the new battery in, clicked the connector in and screwed everything back in place. I turned my phone on and my battery immediately had 70% power, whereas before it wouldn't charge past 37% and kept turning on and off. I've got it charging now and am hoping it works like a brand new phone (since I previously factory reset it to try and fix my old battery)!