There are a lot of third-party repos in that zip file. Just saying.
If rpm -qa|grep mplayer didn't return anything, it isn't installed. Once yum is working you should be able to say
yum install mplayer
and it should work fine. However, this is a problem with some installations of FC5. I installed FC5 for a few days before going back to FC4 (the last straw was no flash support) and had this problem. Unfortunately, I forgot what I did. If yum gives you the same error after unloading that file, tell us the contents of fedora-core.repo. You can use
or if you don't want a terminal,