Two females and two males died at the scene in the Keyham area of the city, the force said, along with another male who is believed to be the offender.
Another female was treated at the scene for gunshot wounds and later died in hospital.
The force said next of kin have been informed and it is not looking for anyone else in connection with the incident.
It confirmed the incident was not terror-related.
Local MP Luke Pollard said more people were being treated for their injuries in hospital, and tweeted: “I’m utterly devastated that one of the people killed in the #keyham shooting was a child under ten years old.”
Emergency services were called to Biddick Drive in the Keyham area of the city shortly after 6pm on Thursday.
Witnesses described hearing gunshots with one saying she saw a man “randomly” start shooting at people.
In a statement early on Friday morning, Devon and Cornwall Police said: “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.
“All of the next of kin of the deceased have been located and informed by Devon & Cornwall Police officers.
“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.”
The force added investigations are continuing and there will be disruption to roads in Keyham throughout the night.
It urged the public with mobile phone footage of the “immediate aftermath” of the incident not to post it on social media and to “respect those families who have lost loved ones this evening”.
Police officers and marked patrol cars were stationed at cordons on Thursday night on roads close to the scene of the incident.
Scenes of crime officers in white suits could be seen using cameras in the street.
Members of the public who lived locally were not allowed into their homes.
One witness, who lives near Biddick Drive 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.”
Robert Pinkerton told the BBC he had “walked around the corner” and “bumped into a bloke with a shotgun”.
Mr Pollard tweeted that police had confirmed six had died in the incident, adding “more people are being treated for their injuries in hospital”.
He said: “Just so unspeakably awful. My condolences and thoughts are with the families.”
In a video posted on Twitter earlier, Mr Pollard, MP for Plymouth Sutton and Devonport said Ford Primary School and St Mark’s Church on Cambridge Road in Keyham would be open from 9am on Friday and he, along with police and local councillors, would be attending to support the community.
He said “time and space” will be needed “to process what has happened tonight”, but “this will be a safe space for the community to come together”.
The South Western Ambulance Service said it was called at just after 6pm on Thursday and responded with a “significant number of resources”, including Hazardous Area Response Teams (HART), multiple ambulances, air ambulances, multiple doctors and senior paramedics.
Home Secretary Priti Patel tweeted: “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.”
Labour leader Sir Keir Starmer tweeted: “There’s much we don’t know about the shocking events in Plymouth. However it’s clear tragedy has hit Keyham.
“My thoughts are with the families and neighbours of those caught up in this nightmare. I pay tribute to our emergency services who ran towards events we’d all run from.”