You don't - Fedora Core 5 is legacy now. Install fedora 7 or 8. I'm not even sure that FC5 installer can see usb drives - I recall that installing to sata was funny.
The basic process is as follows - set your bios to boot from ODD then USB then internal.
Plug the drive in, insert install media, reboot.
Use the advanced configuration in the partition section to install linux to the external drive - put grub in the external drive mbr. So, if the drive is plugged in, the bios starts grub. If in ain't plugged in, it starts whatever bootloader is in the internal mbr.
That should be it.
For less recent distros you have to make a small partition on the internal drive to load the usb drivers for the full boot.