A 12-year-old boy, two 15-year-old boys and two men, 24 and 28, were killed in the smash, according to West Yorkshire Police.
Officers were called to Stonegate Road in Meanwood at 9.54pm on Saturday.
Two 15-year-old boys are in custody and the families of the dead have all been informed, police said.
The crash involved a stolen Renault Clio.
Stonegate Road is still closed and the police major collision inquiry team is investigating what happened.
Anyone with any information is asked to contact West Yorkshire Police on 101.
A spokesman for the force said: "At 21:54hrs on Saturday 25th November Police were called to a road traffic collision on Stonegate Road, Leeds where a stolen Renault Clio had collided with a tree. 5 males aged 12yrs, 15yrs, 15yrs, 24yrs and 28yrs have sadly passed away as a result of the RTC and two 15 year old males are in Police custody.
"Family of all the deceased have been informed.
"The road remains closed and West Yorkshire Police MCET (major collision enquiry team) are conducting an investigation into the exact cause of the collision."