That is probably an mpeg2 video file. By run you must mean play rather then execute.
You will need to install a player progam like mplayer or xine, along with the dependencies, from a repository that has the rpm packages built with dvd playback support enabled.
Here is a www.tldp.org
howto on DVD Playback. The web links are for an older Fedora Core, so you will need to locate a more recent directory containing the repository for Fedora Core 5:
It gives instruction on how to add a repository so that you just need to use yum to install these packages.
This site may have a "sticky" post as well, with more recent repositories.