Festival Cruises' "European Vison" visits five ports on a seven-day cruise out of Santo Domingo, with only one day at sea. There are two different itineraries. The company is marketed as First European Cruises in the U.S.
Just about any cruiseline - Royal Caribbean's Serenade of the Seas, Norwegian's Sky (I think), Carnival, and I think princess all hit five amazing Southern Caribbean islands in seven days.