The accident took place on the Jammu-Srinagar National Highway when they were going from Srinagar to Jammu, they said.
The car skidded off the highway and fell into the 400- feet deep gorge near Shaitani Nallah in the Banihal belt tonight, a police officer said.
In the mishap, four Army personnel died on the spot and one was injured, he said.
The injured has been admitted to the Sub-Divisional Hospital in Banihal, the officer said.
The jawans were reportedly posted in Tral in South Kashmir with the Jammu and Kashmir Light Infantry (JAK LI).