If it's slipping in 5th and 6th it's properly had it.
I've only noticed slip in 4th up a steep hill at 3500rpm, and that was after a remap.
For a standard car to slip in 5th/6th @ 55K, someone has either coated the friction disc in KY jelly, or some pretty sh1t clutch control has occurred over a long period.
As useful as KY is for solving friction related issues, I'm waging on the latter. Some people should just take an automatic test and spare the public who possess brain cells of the torturous sound of mechanical abuse.