The best way, in my opinion, would be to use Tiffany Towncar (limo service). For 5 people, it would cost you less than Mears Shuttle and be much more convenient.
The VERY cheapest way would be to take public transportation. It's time-consuming but costs very little.
There are other options, too, including a rental car. It's all explained in detail here:
DH & I were facing the same dilemma. This is our first trip to WDW and our first trip traveling without our car. We chose to take Tiffany Towncar because we did not want to waste the time it would take for the Mears Shuttle to stop at other resorts. For us it was only about a $20 difference. But look at the bright side how often do you get chauffered.
I would only recommend Tiffany to you. We are a family of 4 and it was slightly cheaper to use Tiffany Town Car rather than the Mears Shuttle. Tiffany picks you up right at the airport, you have to go find a Mears bus. Tiffany will take you directly to your resort and the drivers are quite informative (at least ours was). Mears stops at other Disney properties and depending on your hotel (we were Fort Wilderness) you could stop at all of them. With Mears we were picked up HOURS before our flight I think we were on that bus forever. Tiffany will get you to the airport when you are ready to get there
Also on the Tiffany web site there might still be a coupon for $10 off a round trip