My iPhone 5 was basically perfect except that the battery wasn't holding charge for more than a few minutes.
Epic Fail! Took hours and hours to do, mainly because everything is so delicate + tiny so you need to be careful and precise. Also, the battery is difficult to get out and next time I would look at using heat to loosen it as recommended by a few people here.
I managed to do the whole procedure eventually but the home button now no longer works!
Here are the main problems I had:
1. Bloody difficult to pull/pry open the front screen using suction cup and plastic tool.
2. Really hard to get the original battery out as it was stuck down so well. Only later did I read the comments about using a little heat to make it easier to remove the battery.
3. It was tricky refitting the 3 ribbon cables at the top of the phone.
4. It was even harder to refit the metal plate covering these 3 cables. You have to kind of hook it in which is difficult when the 3 cables are in place. I ended up putting it in place without the cables first just to get familiar with the fitting.
Finally managed to finish it after several hours. The battery seems fine now but the home button doesn't work!
I would say proceed with extreme caution or pay a professional to replace the battery.
Agree with other comments about using a little heat to make battery easier to remove. Also, fit cover without cables to get familiarised with the fitting.