Aha! It's not just MY Palm Tungsten T5!
Had a very difficult time getting my Palm Tungsten T5 to synch with my computer, even going so far as to buy a new desktop system (I needed a much faster one anyway).
Took me months and a few aborted calls to Palm's unfriendly, unhelpful "tech support" before I stumbled on the solution.
Turns out the USB connector was so finicky that I had to lay the T5 on the desktop sans case, plug the cable in, pushing it in tight, and ensure that the cable did not pull the connector at all.
Someone else had the same problem.