Feyenoord dominated the match in every department and were 3-0 up at half-time thanks to goals from Igor Paixao, Yankuba Minteh, and David Hancko to the delight of the home fans in De Kuip.
The second half was a procession for Feyenoord, who seemed able to cut open the Ajax defence at will, Paixao and Minteh each netting a second, the latter with a sweetly curling strike.
Quinten Timber completed the humiliation and Feyenoord could have had a seventh but the goal was ruled out for offside.
It was a record margin of victory for Feyenoord in a Dutch Klassieker, topping the 9-4 win from 1964.
Four-time European champions Ajax have endured a catastrophic season both on and off the field.
They had their worst-ever start to a Dutch top flight season, briefly propping up the Eredivisie table, with fans' frustration boiling over into violence.
The club of Johan Cruyff, Marco van Basten and Dennis Bergkamp, Ajax have fought back somewhat since those dark days but still sit in an unfamiliar sixth place in the Dutch top flight.
They are 31 points behind runaway Eredivisie leaders PSV Eindhoven and European football looks a distant prospect next season.
To make matters worse, the club revealed two embarrassing financial slip-ups this week.
On Tuesday, they announced they were suspending CEO and chairman Alex Kroes on suspicion of insider trading.
Kroes bought more than 17,000 shares a week before his appointment was announced on August 2, 2023.
And on Friday, it emerged that club chairman Michael van Praag, who had vocally criticised Kroes during the week, had "forgotten" to declare his own shares in the club to the correct authorities.
As for Feyenoord, they enjoyed an extraordinary double over their rivals, having beaten them 4-0 away earlier in the season.
They sit second in the table, nine points behind PSV.
