How to factory unlock a contract at&t iphone 5s?

Thanks.

Added (1). I don't have the sim card for the iphone 5s as I got one for my Galaxy S4 instead. Hopefully that isn't a problem

The fastest way is to order an unlock from Kesy2iPhone. They unlock any AT&T iPhone including the new iPhone 5S. Or contact AT&T directly and request an unlocking code.