The terrorists fired upon the vehicle at around 3 pm near the Bhimber Gali area.
The vehicle later caught fire due to a likely grenade attack, the Army said.
The unidentified terrorists fired at the Army vehicle, taking advantage of heavy rain and low visibility in the area, an official statement released by the Army headquarters, Northern Command, said.
"The vehicle caught fire, due to likely use of grenades by terrorists," it added
The five deceased personnel belonged to the Rashtriya Rifles unit deployed for counterterrorist operations in the area, the Army said.
Another soldier, who was seriously injured in the attack, was evacuated to the hospital and is under treatment.
Operations are on to locate the attackers, it added.
"Anguished by the tragedy in Poonch District (J&K), where the Indian Army has lost its brave soldiers after a truck caught fire. In this tragic hour, my thoughts are with the bereaved families," said Defence Minister Rajnath Singh.
Anguished by the tragedy in Poonch District (J&K), where the Indian Army has lost its brave soldiers after a truck caught fire. In this tragic hour, my thoughts are with the bereaved families.
— Rajnath Singh (@rajnathsingh) April 20, 2023
The terror attack comes ahead of the G20 Tourism Working Group meeting scheduled in Srinagar in May.
Last week, Union Home Minister Amit Shah and National Security Adviser Ajit Doval reviewed the security situation in the Union territory.