The attack on Saturday came hours after six villagers were killed in an attack elsewhere in the region.
The gun and grenade attack on a highway linking Srinagar and Jammu - the two main cities in Jammu-Kashmir state - came as the military convoy passed through Awantipora town on Saturday, army spokesman Lieutenant-Colonel V K Batra said.
Three soldiers died on the scene, while two others succumbed to injuries at a hospital.
Three more soldiers, wounded in the attack, were being treated, he said. Shortly after the attack, Pakistan-based Lashkar-e-Tayyaba claimed responsibility in a telephone call to Current News Service, a Srinagar-based news agency.
Lashkar is the fiercest of more than a dozen guerrilla groups fighting security forces in Indian-controlled Kashmir for the Himalayan region's independence or its merger with Pakistan.
The 15-year insurgency has claimed more than 66,000 lives, mostly civilians.
The attack in Awantipora, 140km north of Jammu, came hours after suspected Islamic fighters attacked a mountain village, killing six people and wounding eight others.
The rebels raided the village of Darmarhi on Friday night, opening fire on the family of two police officers who were sleeping at the time, said an officer in Jammu.
The hail of bullets lasted nearly 15 minutes and left eight family members dead, including an infant and a 4-year-old child, said the officer, who did not want to be named because he is not authorised to speak to journalists.
Eight others were wounded.
The attackers fled the village after the assault, he said, blaming the assault on separatists. His claim could not be independently verified.
Fighters often attack civilians, suspecting them of being police informers.
No group claimed responsibility for the attack in Darmarhi, about 150km north of Jammu.