Peter Young, 47, of Tamworth, Staffordshire, was trying to 'jump the queue' by switching from the centre lane into the inside lane before it was closed, it was alleged at Hereford Crown Court.
But the four-ton Volvo lorry, travelling at 61mph, crashed into the back of the nurses' Ford Fiesta, moving at 15mph between the 800- and 600-yard road work warning signs, Graham Cliff, for the prosecution, told the court.
He said: 'For some reason Mr Young didn't brake. His Volvo ploughed into the Ford Fiesta, crushing it. It rode up over it and drove along the motorway with that car underneath it.'
He said the impact pushed the car into a Ford Sierra in front and caused a six-vehicle pile-up on the east-bound carriageway near Tewkesbury, on 14 July last year.
All the nurses and a passenger in the Sierra died at the scene.
Mr Cliff said Mr Young, who denies five charges of causing death by dangerous driving, had begun work late because he overslept and was further delayed by traffic jams. The crash happened as he headed home in the afternoon. He said Mr Young was 'in a hurry, seeking to make up a little bit of time'. He said he overtook three lorries, then 'instead of waiting to go through the lane closure, he was trying to jump the queue . . . He was trying to cut up on the inside of slow moving traffic. It led to a horrendous collision.'
The nurses, who worked at the Bupa South Bank Hospital in Worcester and were returning from a training day in Cardiff, were Corrie Howard, 32, Pauline Edwards, 45, Liz Crooks, 46, and Sheila Corbett, 48, all from Worcestershire.
The victim in the Sierra, who was returning from holiday in South Wales, was Elizabeth Cruickshanks, 61, of Strathclyde.
The case continues.