Arpad Kore and Bartosz Bortniczak, both 18, and Jordanna Goodwin, Megan Storey, and Blake Cairns, all 16, died in the crash in South Yorkshire.
Their car collided head-on with another vehicle on the A630 near Conisbrough on 15 November, 2014.
Doncaster coroner Nicola Mundy ruled that each of the five teenager's deaths was accidental.
The other car driver was injured.
Jonathan Earp was in a car ahead of the Toyota Corolla at the time of the crash.
Giving evidence at the inquest, he said when he got to the vehicle all the teenagers except his friend Arpad Kore were unconscious.
"He was screaming out in pain and begging me not to leave him," Mr Earp told the court.
He said he was unable to open the car doors and held his friend's hand until the emergency services arrived.
Ms Mundy said she agreed with collision investigators that the most likely cause of the accident was that Mr Bortniczak took his foot off the accelerator as he negotiated a right-hand bend, causing a classic case of "lift-off over-steer".
The car, which had been travelling at about 73mph in a 60mph zone, skidded and was side-on when it hit the Seat.
Tests showed the car would have been able to safely take the bend at that speed if the driver had kept his foot on the accelerator.
Recording her conclusion, Ms Mundy said: "It was the most tragic of accidents. Five young people, who had their lives ahead of them, losing their lives in these circumstances.
"I do not think there were any signs of recklessness. It was a mistake and a high price was paid for it."
The crash happened after the five friends met up with two others - Ben York and Jonathan Earp - who were in a Vauxhall Corsa.
The court heard there had been an investigation into whether the cars had been racing after one witness, Michael Staton, said he had seen two unidentified vehicles at traffic lights revving their engines and then "set off like a dragster start".
Mr York, the driver of the Corsa, was arrested on suspicion of causing death by dangerous driving but never prosecuted.
But the coroner said: "I do not think there's evidence of them racing or being reckless on the road."
Ms Mundy said she would be writing to Doncaster Council to ask it to consider moving the transition from 60mph to 40mph on the A630 further away from Conisbrough.

The Austrian film-maker was also named best director, while the film's star Emmanuelle Riva won best actress.
The French-language drama tells the story of an elderly couple dealing with the aftermath of a devastating stroke. It previously won Cannes' Palme D'Or.
Daniel Day-Lewis was named best actor by the panel of 60 critics.
He received his award for playing America's 16th president in in Steven Spielberg's historical drama Lincoln.
The movie, which will be released in the UK on 20 January,  also won best screenplay.
Amy Adams was chosen for the best supporting actress accolade, for her role in The Master, while Matthew McConaughey received best supporting actor for his films Magic Mike and Bernie.
The National Society of Film Critics includes some of the most prominent movie writers in the US, including Roger Ebert of the Chicago Sun-Times and Kenneth Turan of the LA Times.
They gathered at the Lincoln Center in New York to choose their winners, with the evening dedicated to the memory of Village Voice critic Andrew Sarris, a founding member of the society, who died last year.
Elsewhere, the Houston film critics' society named Ben Affleck's political thriller Argo its favourite film of the year. Jennifer Lawrence picked up best actress for comedy-drama Silver Linings Playbook while Day-Lewis again won best actor for Lincoln.
Critics' awards are seen as key steps towards the Oscars.
Members of the Academy of Motion Picture Arts and Sciences had until Friday night to cast their ballots, with the nominations announced this Thursday, 10 January.
A teenager has described how his friend, killed alongside four teenagers in a car crash, begged him for help.
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Michael Haneke's heartbreaking drama Amour has been voted the best picture of 2012 by the US National Society of Film Critics.