can't tell exactly. What I can tell is, that CS5 and CS5.5 is running flawlessly on OSX 10.7.5. Also CS6, CC and CC 2014.2.
For running CS5.5 (and other, older software), I left that OSX on my machine and installed the newer OSX 10.10 (not El Capitan!) on a second partition, because all current CC 2015 software will run only on OSX 10.9 and above.
But I think, you should search the forum, if someone successfully is running CS5 and CS5.5 on OSX 10.9.5.