The victim was found with gunshot injuries in Markham Avenue at around 21:00 GMT on Monday and died later at Leeds General Infirmary.
West Yorkshire Police said three men aged 17, 19 and 20 had been arrested on suspicion of murder.
Two boys aged 15 and 16 were detained on suspicion of perverting the course of justice.
Detectives found the victim's Vauxhall Astra abandoned in Pasture Road, near to Back Airlie Avenue.
Det Ch Insp Steve Snow said the force believed the man was deliberately targeted and the shooting took place near to where the car was found.
Five people have been arrested after a 33-year-old man was shot in the Harehills area of Leeds.