And as stated, you can't install it under Catalina but could from an older OS (just boot off it, install), then once you reboot into Catalina, it should run with the caveats outlined. It is totally unsupported under that OS!
Author “Color Management for Photographers" & "Photoshop CC Color Management/pluralsight"
"Is it worth trying to install an older unsupported version of Lightroom"
Anything earlier than Lightroom 6 (and including Lightroom 6) has the same problem, it cannot be installed on Catalina. You would have to install it on an earlier operating system (and this assumes you have the 64 bit version of Lightroom because the 32 bit version of Lightroom will not run on Catalina, even if you can install it on an earlier operating system)
I thought (although my memory may be wrong) that Lightroom 5 came in both 32bit and 64bit versions. The 32bit version definitely won't run, even if you could install it on an earlier OS.