Adobe CS 5 Production Premium mac-windows Installation issues

Hi there community!

I own a copy of Cs 5 Production Premium for Mac OS, I used it on my mac laptop for years but have now switched to a desktop running windows. I'd like to install the same copy on my new computer but the discs don't work. I downloaded the windows version of Production Premium cs 5 from the website but when i put the serial key in it said it wasn't valid. I'm not sure if I've downloaded the wrong collection of not but it seems ridiculous if the serial key is operating system specific!

Hoping for help! I've got projects and deadlines and need these programs to work! Thanks.