Where do I find legacy updates for Adobe CS5 (Illustrator) so that it can be compatible with 64 bit MacOS processes?

Adobe Illustrator CS5 has not been supported by Adobe for a very long while. Even if parts of it were possibly 64-bit, it was never made entirely 64-bit, and you should not upgrade macOS beyond Mojave if you expect to continue using the older, non-subscription Adobe applications.

For future solutions, you may want to consider the 64-bit Affinity Designer, or Pixelmator Pro as Illustrator replacements. They are both available without subscription for little money in the Mac App Store, and each vendor site has a free trial for you to explore.

From beta testing Catalina, I can tell you the CS6 apps will not run. You get a message with any of them that the app is not supported in that OS. Knowing that, it's pretty much a given CS5 will also not run beyond Mojave.

One thing needs to be mentioned. You do NOT have to upgrade to Catalina. You can stay where you are with no ill consequences. If you are running Mojave you will continue to receive security updates for some time to come. The only time you will be forced to use Catalina is if you buy a new Mac after Catalina is released.

The place to find Adobe product updates is from Adobe.

You will need to upgrade to a newer version of Adobe software.

About the only way you could do that in Catalina and forward is to run a VM such as Parallels, VMware or VirtualBox. Run an older version of macOS within that to run the CS5 apps.