About 1,400 passengers were aboard at the time, but none were involved in the accident on the Thomson Majesty, berthed at the island of La Palma.
Thomson Cruises confirmed the incident, saying: “There have sadly been five crew fatalities and three crew injuries.”
All of the dead were men – three were from Indonesia, one from the Philippines and the fifth from Ghana.
One of the three injured was discharged from hospital, with the other two also expected to be allowed to leave shortly.
The injured were also all men, two aged 30 and another, a Greek national, aged 32.
Investigators were trying to determine what caused the lifeboat to plummet into the water before capsizing.
Rescue personnel were called to the dockside after “a lifeboat with occupants had fallen overboard from a cruise ship docked at the pier of Santa Cruz port in La Palma”, a regional government statement said.
A small, white two-hulled lifeboat could be seen capsized beside the ship.
The Thomson Majesty had been due to sail yesterday afternoon to the port of Funchal on the mid-Atlantic island of Madeira.