A report published on Tuesday by The Tribune stated the incident took place on Monday evening.
Reportedly, the incident occurred when the driver of the car lost control and fell into the deep gorge.
The report quoted police sources as saying that the car was going from Namchi to Kaluk, a tourist destination, which is located amidst the mountains of West Sikkim, at an altitude of 5600 feet in Sikkim.
Namchi is the district headquarters of South Sikkim in Sikkim.
It has also been reported that the five deceased belonged to West Bengal’s North 24 Parganas district.
Four of the deceased, as per the report, were of the same family.
The three critically injured persons, including the driver, have been admitted to the hospital.