highway vibration
The 5 minute delay is strange. Can't think of anything in the drivetrain that might cause that other than maybe a lean fuel condition due to fuel boiling, etc. However, you shouldn't feel a rough engine in the steering wheel.
Maybe a tire tread is delaminating. It takes time to heat up and swell a bubble. I had that on my '82 Chevy S-10 w/ crappy Uniroyal tires from the factory. All 4 tires had the tread come off in chunks before 20K miles. That caused severe vibration on the highway.