A towncar will not have enough seats for 5 passengers. You would have to rent a limo or take a shuttle bus to you resort if you do not rent a car.
Alamo is located inside the airport, so there is no need to take a shuttle to an offsite location to fill out your paperwork and pick up your car.
Depending on your length of stay and the class of car that you're renting, the cost of the rental can be the same or less than having limo service. And sometimes 2 single-day, one-way rentals can add up to the same price as a week-long rental.
For example:
For our next trip, a week-long rental of a full-size from National is going to be $109. A towncar service would cost us $90 plus tips. Two one-way rentals would cost us $96 and it would be for intermediate-size cars.
If you're staying onsite after May 5, you could take the Magical Express for free.