Store cards count towards 5/24 if the card can be used everywhere (for example, a Macy's AMEX card). Usually, if the store card is a Visa, Mastercard, or American Express, then it will count. As for store cards that can only be used inside the particular store, it's a little questionable right now. There are reports that Chase is getting stricter with this, so it's best that you skip the store card offers at checkout.