It happened around 3am today after a blue Volvo V60 failed to stop for officers on Tempest Road in Beeston.
Within a short space of time, the car, which had three men and two women inside, hit a house in Flaxton Gardens.
All five were arrested on suspicion of conspiracy to commit robbery. One of the men was also wanted on re-call to prison.
All five were taken to hospital for treatment for injuries, including a fractured arm and a fractured wrist.
Four rescued from car after it hits Leeds house.The person inside the house was moved to alternative accomodation after an inspection by a structural engineer from Leeds City Council.
Two males thought to be either Eastern European or Asian in a white van are believed to have been in an altercation with the blue Volvo on Beeston Road shortly before police spotted the vehicle and are believed to be key witnesses.
Officers are appealing for them or anyone with information to come forward.