The teenager, who cannot be named, appeared before Leeds Youth Court over the collision on Stonegate Road, Meanwood.
The boy had bruising and cuts to his face and his arm in a sling when he appeared in the dock of the court.
The slightly-built, dark haired teenager wept as he sat between two dock officers during the 20-minute hearing. His parents sat in front of the dock.
The defendant, who cannot be identified, spoke only to confirm his name, age and date of birth.
The charges relate to the deaths, on Saturday November 25, of Ellis Thornton-Kimmitt, 12, Elliott Thornton-Kimmitt, 14, Darnell Harte, 15, Robbie Meerun and Anthony Armour, 24. All are from Leeds.
District Judge Marie Mallon told the teenager he should indicate to her if he did not understand any part of the court proceedings.
None of the charges were put to the teenager.
His solicitor, Stephen Smithson, told the court he needed more time to speak to the boy and his parents before any pleas could be indicated to the court.
Prosecutor David Holderness gave brief details of the alleged offences as he made an application to remand the defendant into custody.
Mr Holderness said the car involved in the collision had been stolen earlier on the day of the incident after a members of staff at a Wilkinson’s store had her keys stolen from behind a till, at around 4pm.
The fatal collision took place later that day at 9.50pm after it was driven at speed and went out of control.
District Judge Mallon refused Mr Smithson’s application for the teenager to be given bail.
The case was committed to Leeds Crown Court where the teenager will next appear on December 13.
The defendant’s mother wept throughout the hearing. She mouthed the words “be strong” to him as he was led from the dock.