Officially, compatibility for CS5 ended at El Capitan or maybe it was Maverick, I can't remember. As to whether or not it will run on High Sierra or Mojave is anybody's guess. It might work or it might not. That's the risk you take with outdated, unsupported software.
I can tell you for certain that Creative Suite won't run on Catalina which ended support for 32-bit apps.
Yes, Creative Cloud products can open older CS files.