Yes, download LR 5.7.1 for Mac from Adobe.com, install it, and enter the serial number (if you had bought an upgrade to LR 5 from a previous version, you'll also need the serial number of the previous version). You don't need to deactivate the license on the Windows machine.
Install the latest version by downloading it from Adobe's site.
When prompted enter your serial number.
The license is cross-platform.
Brilliant, thank you both for your prompt responses. Sounds pretty straight forward to me