OP, you didn't describe your group. Or what activities you have planned for that day.
A family of 5 could be 2 adults and 3 very young kids, with the kids being difficult for one parent to handle on their own. Or it could be 5 adults.
For example, if you have 5 adults: 4 could go from Riviera to a theme park by Disney transportation. One could get in a cab with perishable food items (or all of the luggage) and go to Boardwalk. After leaving everything with Bell Services at Boardwalk, this person could then take Disney transportation to meet the others at the theme park.
If your plan was to have everyone just hang out at Boardwalk that day: if you have 5 adults, 4 could take the skyliner from Riviera to the Epcot International Gateway entrance, and then walk to Boardwalk from there. One could get in a cab with perishable food items (or all of the luggage) and go to Boardwalk.
I don't think you would need a cab big enough for your entire group unless your people can't/won't split up.