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.
The person inside the house was moved to alternative accomodation after an inspection by a structural engineer from Leeds City Council.
Two men 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.