My iPhone5 was having the short battery life problem where the battery drops rapidly and sometimes will go from 40% to less than 20% or shut down all of a sudden without warning. Running my serial number through apple's website, it shows to be eligible for a free battery replacement. However my phone was jailbroken and I didn't want to wait for the store/shop to repair so I did it myself by ordering a battery from iFixit. Followed the guide for the replacement and now my phone pretty much lasts me through the day. Points to take caution is removal of the battery connector from the socket and removal of the battery from the chassis. Dont stress on the motherboard components for leverage when prying on the battery, it might be helpful to heat the back of the phone with a hairdryer instead to soften the double sided tape that holds the battery. Also to make it easier to grab the plastic battery removal tab, I stuck some tape on the tab to make it longer which I found to be much easier to get a grip on it.
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