Disclaimer: I really don't know. Just my two cents. . . .
I too have a Palm Pilot and OE 5.0. I had already installed my Palm desktop when I started using OE, and I went to look into syncing with OE. However, I remember reading documentation that syncing with OE DISABLES the palm destop syncing. i.e., when you put your palm in the cradle, OE will take over, and your Pilot will never again sync with the palm desktop (unless you turn off syncing with OE).
However, this was a number of months ago, and OE has been updated twice (from 5.0 - 5.02), and the palm software has been updated a number of times. My guess would be that they're both fighting over access to your Pilot. Have you tried disabling the palm desktop to see if things work out between the Pilot and OE?
In my case, I decided to only sync between the Pilot and the Palm Desktop -- with it's calendaring, etc., etc., and then do a one-way dump of my contacts, etc., in OE about once a month. There are at least a couple of scripts available that work just great. And I do that once a month or so. I've had no problems.
Anyway, hope that helps a bit. Good luck.