Creative Suite serial numbers are Mac only or Windows only.
One option is to pay for a cross-grade to CS6 for Mac. Won't work on your PC though.
Or join the Cloud and then you can install on both Mac and Windows.
All Creative Suite products are platform specific. You would need to upgrade to CS6 and request a platform swap from Adobe or buy the subscription for the new Photoshop CC. With the new CC version, they are not platform specific, meaning you can use it on Mac and PC.
For CS6, click buy then upgrade: Creative Suite 6