No, Little Snitch 5 cannot be used on macOS Catalina. It requires macOS Big Sur or later. If you want to use Little Snitch on Catalina, you have to install version 4 instead.
Little Snitch 5 is based on Apple’s Network Extension framework, which replaces the previous kernel extension API, that is no longer supported on macOS Big Sur.
This framework is quite new. Although it already exists on macOS Catalina, some of the API that Little Snitch relies on was added to this framework only with the latest Catalina updates, still containing some bugs that have only been addressed in macOS Big Sur.