AMEX cardholders need to ensure that their card is set up as the default billing method within iTunes itself. Once a $5 purchase is made and charged to the American Express card, a $5 statement credit will appear on their account.
American Express runs a number of these promotions, though availability does vary based on previous card usage. Some users may not be able to see the iTunes promotion because of how they use their card, for example.OFFER DETAILS
Spend a total of $5 or more on iTunes using your enrolled American Express Card by 4/30/14 and get a one-time $5 statement credit.
Article Link: American Express Offers $5 off a $5 iTunes/App Store Purchase