Javarney Drummond, 15, Niko Hill, 15, Jack Wallace, 16, Joseff McCarthy, 16, and Andrew Goodger, 15, were killed when the car crashed.
The five passengers died instantly while Fleming received moderate injuries.
Fleming was initially charged with five counts of manslaughter but those charges were later reduced. He pleaded guilty to dangerous driving causing death in April.
At the High Court in Timaru on Wednesday, Justice Rob Osborne jailed Fleming for two years and six months.
In his victim impact statement, Andrew's dad Richard was emotional as he described his son as a "perfect young lad" who made a tragic mistake.
"It was hell the night my son never came home," Richard Goodger told the court.
"Since Andrew was killed I am living in absolute hell."
Niko's mother Carissa said her world was thrown upside after losing her son.
"This pain I feel is like no other pain," she said. "I now have to live with this deep dark pain."
Crown prosecutor Andrew McRae said the crash was a "combination of very poor decisions" by Fleming.
Through defence lawyer Thomas Nation, Fleming said he was angry and ashamed by his decisions.
"He asked me to say: To all the families... I will forever be truly, truly sorry," Nation said.
In his summary of facts, Justice Osborne said Fleming's dangerous driving took the lives of five teenagers.
"All your passengers were killed instantly," Justice Osborne told Fleming. "You survived."
In addition to the prison sentence, Fleming was also disqualified from driving for five years.
"It is the only appropriate sentence - it is the only appropriate outcome - for the harm you have done," Justice Osborne said.