Is opening 10 operating compatible with Photoshop CS5 EXtended?
You should actually ask they question the other way round, i.e. if Photoshop CS5 is compatible with Windows 10.
Officially it is inexpert and not likely to be. CS5 is relatively old and predates the contribution model Adobe now use so they will have no interest in keeping it going. Adobe CS has always been a bit finely tuned to permissions issues and there were large
changes. Some report it still running after a Windows promote with it already installed, how it would behave if at all on a clean install could well be different.