Thettayil said the five cadets had told officers of the National Cadet Corps that they were going to the Periyar river to take photographs.
While three of the cadets were reportedly brought dead, the other two died in the hospital.
He said the names of the five were not yet known but they were said to be attached to the NCC Delhi unit.
Students from 16 states are taking part in the national trekking camp that began Dec 23 at Malayatoor, a place known for hilly terrain.
Witnesses said the bodies were taken out of the river by forest and fire service officials with the help of locals.
"We are given to understand that they did not venture for a swim but fell from the river bank into the river. The place is treacherous and only experts can manage to swim," Thettayil told IANS.