My iPhone 5's (bought on January 2013) battery life is now something about 5-6 hours. I found some possibilities how to buy new battery and replace it. Does anybody have some experiences with this replacement? Does it work and solve the battery life problem?
Before paying an independent dealer to replace your battery, first check if Apple will do it for free
Enter your serial number on this page - Apple: iPhone 5 Battery Replacement Program
It is relatively simple to replace an iPhone 5 battery. However, there are some tools which are highly recommended you buy first before continuing as you have to remove the display and can break cables in the process.
Local retailers would likely be able to fix your battery for about $45-$50, if you choose to have it services either by an AASP or an unauthorized repair shop.
To do it yourself, check out this guide from iFixIt. It will walk you through step-by-step (with pictures) and you can also buy the battery + all requisite tools via their website.
I myself have performed a battery replacement on a 5 and do recommend the tools.