There are five basins within the Caribbean Sea, they are the Yucatán, Cayman, Colombian, Venezuelan, and Grenada basins. The Caribbean coastline has many gulfs and bays: the Gulf of Venezuela, Gulf of Darien, Golfo de los Mosquitos and Gulf of Honduras.
Five basins you mean these are seas under them?
The Caribbean Basin is generally defined as the area running from Florida westward along the Gulf coast, then south along the Mexican coast through Central America and then eastward across the northern coast of South America. This region includes the islands of the archipelago of the West Indies.