Sorry, but the warranty for the iPhone is only valid in the country where you bought the device.
In most of the cases 3rd party apps or settings caused the battery to drain faster than before the new software has been set up. Sometimes the mail app tried to connect to the mail server over and over again, deleting and setting up the mail account can solve this problem.
In other cases social media apps did similar things to the phone.
Here are some suggestions for getting back the normal battery life, maybe they are helpful for your problem with your iPhone 5 as well.
Check the links provided by Texas Mac Man in this post about battery life: