No. You pay for new versions, your old serial number is only for the product for which it was purchased. If you wanted CS5 or CS6 you would have to pay for them.
With a new OS, Adobe will most likely not consider selling you the newest CS versions anyways. If you have a system capable of running the Creative Cloud software you are limited to purchasing CC plans thru Adobe, or non-CC products.
Installing Creative Suite on macOS 10.12 (Sierra)
https://helpx.adobe.com/creative-cloud/kb/install-creative-suite-mac-os-sierra.html