The teenager, who can not be named, appeared at Leeds Crown Court via video-link where he pleaded guilty.
The crash happened just before 10pm on Saturday 25 November when a Renault Clio ploughed into a tree in Stonegate Road.
At the time police described it as '"catastrophic". They said officers were confronted by "a scene of total carnage" when they arrived.
Ellis Thornton-Kimmitt, 12, his brother Elliott, 14, and Darnell Harte, 15, were the three children who died in the crash.
Robbie Meerun and Anthony Armour, both 24, were also killed.
The teenager, who wept in the dock during a previous hearing, will be sentence on 26 January.