The search for survivors was hampered by two later rock slides that hit the crumpled structure, partly built into a steep hillside in Aalesund, about 220 miles northwest of Oslo.
A propane tank caught fire and was at risk of exploding. Authorities evacuated about 40 houses and apartments in the area.
The bottom floors of the apartments caved in just after 3:30 a.m. when the first slide slammed into the back wall.
"We first thought it was an earthquake," said Lars Aage Eldoey, who managed to escape with his wife from the top floor. When he got out on the balcony he realized what had happened.
"There were enormous rocks - not just rocks - half the hill had slid down into the bottom floors," he told state broadcaster NRK.
Smoke billowed from the twisted bottom floors of the collapsed building, with sagging balconies and a contorted glass entryway.
Rescuers said five people who lived in the apartments were unaccounted for and possibly buried by the debris inside.
"We fear that the missing people are dead," police rescue leader Kjell Kvenseth told the TV-2 network at the scene.
Fifteen people were taken to a hospital, two of them with moderate injuries, Aalesund police operations leader Magne Tjoennoey said.
Tjoennoey said rescuers had not been able to enter the building, which was finished in 2003, to search for the five missing people.
"We have to wait for the propane tank to burn out. That will take time. It's big, with about 4 cubic meters (140 cubic feet) of gas," said Tjoennoey.
Tjoennoey said police had not been able to confirm whether the five people reported missing were in the building, or had not been home at the time of the collapse.
"We have not been able to find out where they are," he said. "As time goes by, we increasingly fear that they are in the building."
A helicopter, rescuers and search dogs from around the region were called to the scene, including the Norwegian unit of the United Nations International Search and Rescue Advisory Group, he said.
"The bottom floors are collapsed. There is a big risk in going inside, and there is also the risk of fire," Tjoennoey said. He also said geologists at the scene considered the risk of further rock slides to be small.