You should deactivate it first on the old hard drive, which frees up the license to be used on the new machine. Upgrading is as easy as a clean install, you'll just need the serial number for the copy you're upgrading from in addition to the CS5 serial.
I agree with the instructions to Deactivate first, the to reinstall and Activate, when done.
While one can do various types of mirroring, and cloaning, many go very, very wrong. Doing a clean install of the OS, and then the programs, is almost always 100%.
Many thanks, I was hoping it would be that simple.
Thanks, I will do a clean install.