Good luck!
As others have said, try the 80-200 on the F5 before selling it. Mine is very useable for most sports on a D700, 750, and F100. Sluggish on the F4, and sometimes hunts.
My experience with it was shooting university sports multiple times per week for about two years, always from the sidelines. That was about a year and a half back. During that time I also used comparable Canon gear, a newer 70-200 as a rental, and some longer teles. The 80-200 was a workhorse and bagged some of the best shots. Obviously MTB is demanding, but aside from the elevation changes it is more or less linear (subject moves towards and then away from camera) whereas something like figure skating or basketball is a little more erratic. One would expect a good AF system to track linear action fairly well.
Please let us know how it goes! I'm curious to see how it turns out.
I am definitely going to try my D lenses on the F5. Based on what I have read, it hammers to focus so they will probably work very well.
I will check back in once I start using it. The race season is over but I will probably take it out and shoot moving cars and things on the highway, just to get used to it.