You can only use up to 4 different methods of payment. So essentially, 3 gift cards + your credit card for the difference.
You may be able to split your party up, paying for one person at a time... but this may not work for all 5 of you if you have children, and one ends up looking like an unaccompanied minor.
An alternative is to use 4 gift cards to buy a refundable ticket somewhere (anywhere). Lets say you buy a $200 ticket with 4 gift cards. Cancel reservation. SWA will give you a $200 credit for a future flight. Now that $200 credit counts as only one form of payment. (Repeat as needed)
I only did this once... just to fly one person. I have a employee discount + red card at Target and essentially get 14% off. It was kind of a pain in the butt for 1 person for 14% off, but still worth it (a smudge).
That said, if I were trying to do the same thing for 5 people for only a 5% discount, no way no how. Not worth my time. At most I would just buy (3) $50 gift cards, save my paltry $7.50 and pay the rest by credit card.