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, downshifted into first to turn around to back into the 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.

I plan to try to disconnect the remote shifter from the connector to the transmission to see if that is the issue, but it is super hot, so I am hoping for some insight before getting swamped.

Please help

It’s locked in 5 when the engine is on and off?

Both. It has less than 0.25 inches of play forward and back and will not go into neutral. I tried move the shifter with the car running and turned off no movement. I tried holding some force on it and bumping the clutch when it was running, but it would lunge forward if the break was off or just die if I held the brake.

Personally, I wouldn't be sweating it until you get eyes on the shifter. You verified the clutch works so it's either internal to the transmission or something is messed up/in a bind with the shifter. You found external debris so chances are it's an external problem you'll see when you get in there. Obviously, there's a chance something more serious is going on but it seems more likely there's an issue with the shifter itself.

Stock shift or aftermarket?

Jack the rear of the car up. Emergency brake OFF. Start the car. See if the tires completely stop with clutch engaged. If they do not, it's either throw out bearing or clutch master cylinder.

If it’s stuck with the engine off, clutch in or out, my bet is the shifter is binding or locked up. Maybe a frozen shift fork.

I would start with the shifter given we have a remote shifter setup with a couple of bushings.

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.

If you already have the shifter out, and decide to upgrade, I always recommend MGW. I have one in my 08 Bullitt.

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.

That sounds like the shifter. Hopefully that's all it is.

Ya! Sounds like the shifter is messed up. The traction light it because the rear wheels are turning while the front wheels are stationary.
With the shifter removed, the shaft sticking out of the transmission should slide in and out and rotate slightly. It does not move easily against the detent inside the transmission.

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