Firmware files for some of our older cameras are no longer available through Canon. Unfortunately the EOS 5D is one of the models that no longer have firmware files available through Canon. Due to that you will not be able to download it through out website and there is not a way to send you the files.
Through Canon support we can only recommend services offered directly through Canon, so cannot recommend non-Canon websites that may have the firmware available or the quality of the downloads from non-Canon websites.
If the newer FW doesn't have a specific feature or upgrade that you need, you do not need to do it. As a matter of fact if you have a perfectly running 5D, I would not under any circumstances chance a FW upgrade. On the chance, albeit slim chance, it goes wrong you will have a brick and Canon can no longer unbrick it for you.
The newer FW may only add languages to the menus for instance. Something most of us don't need. Find out what it addresses to see it is something that affects you and your shooting.
That to me would not be a good reason to try a FW upgrade. I never use CF cards bigger than 16GB anyway. I am of the smaller is better opinion because you have to switch them out more often. That reduces, again perhaps small, chance you lose some photos due to unforeseen circumstances. But I am in a position where losing a photo is not an option. You may not be in that position and it is just an annoyance if you lose a shot or two.
And I never "store" photos on my CF cards. They get formatted at every shoot so a large CF card isn't necessary.
Here is a link where you can download firmware 1.1.1 for 5D Classic. It also has some of the instructions that need to be followed carefully when doing firmware updates. For additional, step by step installation of a firmware update, see any of the newer cameras where the instructions are still online.
You'll need a fully charged battery and a memory card without any photos on it (or anything else that you want to keep, because you'll need to format it in your camera prior to installing the new firmware file on it). It's critical to not interrupt the camera during the installation of the software.