From Fedora Project Wiki

Firefox 5 is now available as an official update for Fedora 15. Tom Callaway has a repository available for Fedora 14 users that want to use the latest release.

Download and place it in /etc/yum.repos.d.

su -c 'wget -P /etc/yum.repos.d/' 

Use PackageKit or run the following command,

su -c 'yum install firefox5'

Note: You might want to remove any other Firefox versions on your system. Although Firefox 5 is parallel installable, running it together with other versions is not recommended.