I really REALLY wouldn't, you'd be much better off doing a fresh install.
Having said that if you really want to, this is what you need to do (as root):
rpm -Uvh http://download.fedora.redhat.com/pub/fedora/linux/core/6/i386/os/Fedora/RPMS/fedora-release-6-4.noarch.rpm
yum -y upgrade
This may not work - if you get loads of dependency errors, then you're much better off installing a fresh copy of FC6.
It's worth noting that you can install FC5 and FC6 side by side and get them to share the same bootloader so you can migrate gradually from one to the other - I tried this with FC6test3 a month or so back and it worked fine. There's a bit of editing of the grub config necessary to use only one copy of the bootloader, but it's not all that complicated.