If your new Mac is running the Catalina version of MacOS (which is likely), you need to be aware that LR5 cannot be installed on that operating system. The installer is 32bit, Catalina will only install and run 64bit applications.
Nothing easy. You could try downgrading the OS to Mojave, but that stops you ever upgrading the OS in future, as long as you still want to use LR5, so I certainly wouldn't do that. Or you could sign up for one of the subscription-based Adobe Photography Plans to run the latest version of Lightroom (now called Lightroom Classic, which is at version 10). Or if subscription isn't for you, you could buy the latest Photoshop Elements....or move to a non-Adobe solution.