This will not be possible without the CD. Probably one of the reasons that Adobe started using the cloud.... aside from all the production and publishing costs, now I can login in from anyones computer download the app, login to use it and have access to all of my files, my Creative Cloud libraries and even my workspaces... all saved under my adobe ID. And I can download and use the application on two computers.
I personally have the Creative Cloud, but you can get the all new Photoshop CC 2018, AND Lightroom CC and Lightroom CC Classic, and Portfolio, and Adobe Spark with premium features ... for for $9.99 a MONTH!! And you also will have access to Lightroom Mobile and probably Photoshop Fix but don't quote me on the last two apps. All that for $10/month and you also get 20GB of storage, use of the new Libraries.....
Check it out!
hope that helps!
CS5 does not run well on anything after OS X 10.8, or maybe after 10.9, i forget exactly. I wanted to run CS5 (an expensive purchase for sure) on my new MacBook Pro running 10.11 but there were issues.
On the plus side, CC 2018 does not require java to install. It does however install 5 million background processes (exaggeration).
It is definitely not supported by Adobe. Try it out though, your mileage may vary.