One officer was being treated for smoke inhalation, but no other injuries were reported to first responders.
Four people killed in the morning violence were adults, and a girl, whose age was not known, later died at a hospital, police Sgt. Trent Crump said. He said police shot the gunman.
He declined to release names or specify the relationships of the people involved, but he said they were a family of five and that the shooter was the brother or son of the victims.
A 911 caller from the home described the shooting as a domestic situation, Crump said.
A fire department spokeswoman says the shooter set the house on fire, which crews extinguished after it flared up for a second time.
Mayor Greg Stanton called it "unspeakable violence" but that the first responders' heroism gave residents reasons to take heart.