Prior to the subscription model (CC and CC2014), all Photoshop licenses were absolutely platform specific, either Mac or Windows. The serial numbers are different for each platform too.
If you upgrade to Photoshop CS6 for $200, you can request a platform swap (also called a crossgrade) and that entails a letter if destruction of your Windows version.
To use PS for Windows, you would need to run Windows OS Parallels on your Mac.
CS5 is no longer supported thus no longer a cross grade qualifying product.
If you join the Creative Cloud, you can install CS6 or CC on Win, Mac or both.