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.
A teenager has described how his friend, killed alongside four teenagers in a car crash, begged him for help.