2008 Mustang Bullitt stuck in Fifth gear

2008 mustang Bullitt manual transmission I have had the car since new, it now has 34000 miles on it. Took it to the car wash about 10 miles from home, country roads and 2 miles of interstate and did not notice anything out of the ordinary. After the automatic wash I returned straight home and again did not notice anything strange. Drove up the driveway in second gear down shifted into first to turn around to back into garage. Stopped, shifted into reverse, backed up 20 feet, shifted back into first, pulled forward, tried to shift back into reverse and could not find it , and the shifter felt weird. Shifted into first and into neutral looking for reverse but nothing. Shifted into fifth and now it is stuck hard in fifth gear and will no longer go into neutral. The car will roll when the clutch is in and my wife and neighbor were able to push the car back into the garage while I held in the clutch with the car running. So I don’t think it is the throw out bearing as the clutch will release.
I also pulled the shifter boot and noticed a lot of white powder around the base of the gear shift on top of the metal plate it passes through.

Please help

I ran out of time troubleshooting this last night. I was able to separate the in-car gear shifter arm from the linkage arm that attaches to the back of the transmission at the right-angle connection, and the gear shift arm moved freely. I reconnected it, but it was still stuck with no change from before. I plan to free up the rear tires and see if they spin while the clutch is engaged. If time permits, I will try to remove the remote shifter assembly and see if I can get the transmission to shift by just pulling/pushing on the linkage arm to the back of the transmission. Thank you for the input. I will report back on what I find.

I was able to get the rear end in the Air. With the clutch in, nothing happens. With the gear shift all the way forward, the car stalls when I let out on the clutch. With the gear shift pulled to the back of the travel about 0.25", the rear tires spin, but I get a traction light, and the car will not rev.

After a long delay due to medical issues, I now have an answer to what happened. I finally found a shop willing to take a look, since it seems shops no longer want to work on manual transmissions these days. The issue was that the bolt that prevents the transmission from shifting into reverse from 5th had backed out, locking the car in 5th and preventing it from going into neutral. A side note, when they were loading the car onto the roll back, the vibration locked the car into 5th and reverse, and we had to be shaken from the roll back. This also jammed the gears in the case and made it harder to get apart, requiring a call to a Ford engineer on the proper way to get the case split open. Once open, they inspected the transmission and found only that this bolt had backed out. As they put the transmission back together, we decided to Loctite that bolt in place so this can not happen again. Thanks for all the help.

Jester67

They said that they have over 20 hours in the repair, but only charged me the original quoted 6 plus parts, so it was not that bad to have the car backup and running. The tech took the locked-up case as a personal challenge. He has been building transitions for 34 years, and this was his first time.