Are you running FC5 then download the FC5 firefox 32-bit rpm and if you have the 64-bit firefox rpm installed remove it first, the updated firefox-18.104.22.168 rpm (and others) can be found here;
I'm currently running the RHEL5Beta1 (updated) which is based on the FC6 work with the 32-bit firefox rpm package with plugins installed (BTW, I'm using the 32-bit firefox to post this message), here's the list (partial I think but close enough to get you close) use it as a reference to get the 32-bit FC5 equivalents;
You don't need to download any package you already have installed, but you need the 64-bit counterparts for the libs (think compat and gnome rpms). You may not want to use yum for this, just download what you need into a common location and use rpm (as root or equivalent) to install after testing to make sure you have everything needed;
rpm -Uvh *.rpm --test
Remove the --test switch when all the requirements are satified to really install.