Apple recently discovered that several units of the iPhone 5 are have reduced battery life. They have launched a battery replacement program and have released a statement that the program is eligible for certain serial numbers and units that were purchased between September 2012 and January 2013. If the phone meets these requirements then the battery can be replaced for free.
This replacement can be done either by taking the unit to an Apple Authorized Service Provider or by contacting their technical support team. Unfortunately, because the phone has to meet certain requirements this program is not eligible for the iPhone 5C or the 5S. Also, if the phone is damaged in any other way which would make it tougher to replace the battery such as a cracked screen, that problem has to be fixed first.
This program started in the United States and China on August 22 and will start in other countries on August 29. These changes and replacements for the phone must be made in the country in which the phone was originally purchased. In addition to the battery replacement program, Apple has also launched a replacement program for faulty on/off buttons which have been reported for certain iPhones. Of course, Apple suggests that before their customers decide to get anything on their phone changed, it would be best to back up all the data on the device.