moving LR5 to a new computer

If you are referring to image files, then yes you will be able to load them onto the new computer. But all the work you did using Lightroom 5 won't be there because that was stored in the catalog that was part of Lightroom 5 and was not applied to the images. So images will be in their original state that they were in when they were first downloaded.

If you can add images to the new computer in the same file structure they were in on the old computer, and then bring the catalog that you were using in Lightroom 5, Lightroom Classic has the capability to upgrade that catalog and then all of your work will still be intact.

Lightroom v5 is (basically) not compatible with Mac Catalina OS.

The installer is 32bit (maybe even Lr5 itself is 32bit- not sure) and Catalina will not install 32bit software.

If Lightroom v5 was already installed before the Mac OS was upgraded to Catalina, then it might work as others have reported, but be prepared for problems.

https://www.lightroomqueen.com/lightroom-macos-catalina-compatibility/

Take a subscription to the Photography Plan (20Gb) with Lightroom-Classic v10.0 (the latest upgrade to your v5), Lightroom-mobile (Cloud based), Photoshop 2021, Adobe Bridge, other Cloud ecosystem features- Album sharing, a Portfolio site.

For US$9.99/month (annual plan) you will not regret having the 'latest' and new features!

I do not know what you mean by- "other folder able to be opened.."