Officials at the Koran college said 23 students and teachers had been in the building in the central town of Kayseri when it fell in. Suspicion centred on reports of a gas explosion.
Two of the five bodies pulled from the debris were college employees and the three others were students.
"Witnesses at the time reported a major explosion, after which the building collapsed," Mehmet Ozhaseki, the mayor of Kayseri, a town to the southeast of the capital Ankara said.
"We have five dead, and teachers tell us there are five we still haven't reached in the wreckage. God willing we will find them alive," he added.
Rescuers had already pulled 13 students, young men of between 16 and 18 years, alive from the rubble of the dormitory and school, which offered courses in Koranic studies.
This is the second tragedy to strike a student dormitory in Turkey in recent weeks. An earthquake in May killed 84 boys at a school dormitory in eastern Turkey.