The victims were on their way to Gauth-Lawandhar village in Chopal Sub Division of Shimla, SDM Sangrah Harbans Negi said.
District officials reached the spot and carried out rescue operations with help from police and locals.
The victims have been identified as Balbir Singh (25), his wife Kanta (22) and their three-day-old child.
The injured-- Babli (38) and Balbir (35)-- have been admitted to different hospitals.
Sirmour district administration has announced an immediate relief of Rs 30,000 for the next of the kin of the deceased and Rs 5,000 to each injured persons, Negi said.