The names and ages of the three men and two women were not released. But police said the three men were brothers and the dead women apparently were the men’s mother and a spouse of one of the brothers.
Two other women and two children managed to escape the home unharmed, according to police.
One of those women told officers the shooting stemmed from a family dispute gone wrong, police spokesman Sgt Trent Crump said.
“Our dispatcher could hear shots fired in the background while that call was coming in,” he said.
“A caller had been able to escape the home at that point, get out and start to give us information.” Sgt Crump said the family had origins in Morocco.
During an hours-long stand-off before the bodies were found, police used a megaphone to try to communicate with the occupants of the home, addressing the family in Arabic.
The Arizona Republic reported that one neighbour said the family owned a transport service.
Because they were allowed only two vehicles in the driveway at any one time, the family purchased a home in an adjacent neighbourhood in order to park their fleet, according to the newspaper. It was not clear how many people fired shots, but police said they were not looking for any outstanding suspects.
Officers discovered the bodies after an hours-long barricade situation in a residential neighbourhood.
Witnesses at the scene said they heard the sound of muted gunshots about an hour after the stand-off began.
TV footage showed several SWAT team officers breaking the glass of a back patio door to enter the home.
The SWAT team used a robot to search the house before sending in a dog and officers, Sgt Crump said.
A police perimeter remained in place well into the night, as investigators documented evidence and detectives went door to door.