About 100 other people were injured in the blaze in the eight-story building in Ashulia, near Dhaka, The (Bangladesh) Daily Star reported.
Police said Sunday the dead included three female and two male workers, the newspaper said.
Police, firefighters and witnesses said those who died were not burned, but suffered fatal injuries when they leaped from the upper floors of the Tazreen Fashion building. About 50 people were rescued from the building's roof.
The fire broke out about 6:50 p.m. on the ground floor and quickly spread to the fourth. Firefighters were still working to extinguish the blaze at 2:45 a.m. Sunday, the Star said.
Abu Naim Mohammad Shahidullah, director general of fire service and civil defense, told reporters an electrical short circuit may have been to blame for the fire, though an investigation would be conducted to determine the cause.