The names and ages of the three men and two women were not immediately 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 that the shooting stemmed from a family dispute gone wrong, police spokesman Sgt. Trent Crump was quoted by AP as saying.
"Our dispatcher could hear shots fired in the background while that call was coming in," Crump said. "A caller had been able to escape the home at that point, get out and start to give us information."
During an hours-long standoff before the bodies were found, police used a megaphone to try to communicate with the occupants of the home.
The Arizona Republic reported that one neighbor said the family owned a transportation service. Because the HOA allowed only two vehicles in the driveway at any one time, the family purchased a home in an adjacent neighborhood in order to park their fleet, according to the newspaper.
It wasn't immediately clear how many people fired shots, but police say they were not looking for any outstanding suspects.
Officers discovered the bodies after an hours-long barricade situation in a residential neighborhood. Witnesses at the scene said they heard the sound of muted gunshots about an hour after a standoff 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, Crump said.
A police perimeter remained in place well into the night, as investigators padded around the scene in booties to document evidence and detectives went door to door.