Three boys aged 12, 15 and 15 and two men aged 24, 28 from the Leeds area were injured as a result of the incident.
Officers were called to Stonegate Road in Meanwood at 9.54pm on Saturday.
Detective Chief Inspector Jim Griffiths is leading the investigation. He said: "This is clearly a tragic incident in which five young people have lost their lives. We are currently investigating the exact circumstances of what happened.
“I would like to take this opportunity to ask anyone who saw what happened or has information about it to call us on 101 quoting log 1859 of Saturday 26 November.”
"Two males aged 15 have been arrested on suspicion of causing death by dangerous driving and remain in police custody.
The road remains closed as investigations continue and the road is likely to be closed for some time.
Heard a loud bang
"Me and my wife were watching TV some time between 9.30pm and 10pm when we heard a loud bang.
"I have seen the car which I believe had an '05 number plate completely squashed.
"Within minutes, dozens of police cars, a fire engine and several ambulances were at the scene.
"We could hear the sirens and see blue flashing lights and that's when we realised something very serious had happened."