My old computer crashed and now I was hoping to install lightroom 5 from my old computer onto my new computer. I am going from an Asus to a Mac.
Lightroom 5 software you own is a multiple platform license, so yes you can install it on a Mac computer.
Download link: Install Photoshop Lightroom
Also, just for your information you can install one license on two computers at the same time however there should be one computer in a use at a time.