The man is believed by police to have been shot dead in a house in Överkalix, 1,000 kilometres north of Stockholm, early on Sunday morning.
The five people arrested will be questioned on Sunday afternoon.
“Two people were arrested this morning and a further three people were arrested at the scene of the crime later during the day,” said Erik Kummu of Norbotten Police on Sunday morning.
It is so far unclear what happened in the house, and police are not revealing the type of gun used or the number of shots fired.
“All we know is that a man was shot. We were alerted to the fact that a person was on his way to hospital with gunshot wounds. The ambulance met the car at Töre, where doctors and paramedics declared that the man was already dead,” said Kummu.
The exact roles of the five people being questioned is so far unclear, police say.