West Yorkshire Police said the incident happened in the Meanwood area of Leeds on Saturday night at around 9.55pm.
A 12-year-old, two 15-year-olds, a 24-year-old and a 28-year-old died in the smash, while two 15-year-olds are in police custody.
The families of the deceased have all been informed, investigators said.
Stonegate Road remains closed while the major collision enquiry team investigates the cause of the accident.
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Officers have not released any details of the reason why the two teenagers are being held.
The crash involved a stolen Renault Clio and the force is working on the assumption all seven people were in the car, a spokesman said.
The road remains closed and the police major collision inquiry team is investigating what happened.