Devon and Cornwall Police confirmed two females and two males were found dead at the scene in Keyham area of the city and a third female died of gunshot wounds in hospital.
The suspected shooter, named locally as Jake Davison, is believed to have turned the gun on himself during the shootout on Thursday night.
“Following attendance at the scene, two females and two males were deceased at the scene. A further male, believed to be the offender, was also deceased at the scene. All are believed to have died from gunshot wounds. Another female treated at the scene for gunshot wounds, died a short time later in hospital,” the police statement said.
“Devon & Cornwall Police would stress this is not a terrorism related incident. The area has been cordoned off and police are not looking for anyone else in connection with the incident,” it said.
Police are asking any members of the public with mobile phone footage of the immediate aftermath of the incident not to post anything on social media platforms out of respect for the deceased.
“My thoughts are with the friends and family of those who lost their lives and with all those affected by the tragic incident in Plymouth last night. I thank the emergency services for their response,” British Prime Minister Boris Johnson said on Twitter.
“The incident in Plymouth is shocking and my thoughts are with those affected. I have spoken to the chief constable and offered my full support. I urge everyone to remain calm, follow police advice and allow our emergency services to get on with their jobs,” tweeted UK Home Secretary Priti Patel.
The local MP for Plymouth Sutton & Devonport, Luke Pollard, described the incident as “unspeakably awful”.
“I’m utterly devastated that one of the people killed in the Keyham shooting was a child under 10 years old,” he said.
South Western Ambulance Service said Hazardous Area Response Teams, multiple ambulances, air ambulances, multiple doctors and senior paramedics were also sent to the scene.
One witness, who lives near the scene and gave her name as Sharron, told the BBC: “Firstly, there was shouting, followed by gunshots – three, possibly four to begin with. This was when the shooter kicked in the door of a house and randomly started shooting… he ran from the house shooting as he ran and proceeded to shoot at a few people in the Linear Park up from the drive.”