For users of Fedora Core who have upgraded to FC5, you may want to upgrade to flash-plugin-7.0.63-1 which properly handles integrating with firefox-1.5.x contained in FC5.

http://macromedia.mplug.org/
I have an official agreement with Macromedia to repackage their binary for easy integration into Fedora and make it available in a yum repository here. You can easily keep up with this and future security updates by adding this yum repository to your /etc/yum.repos.d/.