Just try to install CS5 on the new laptop.
If you get a message about activations exceeded then contact Adobe, explain the situation and get the activation count reset.
Thanks, it is an obvious move but I don't want to Adobe to freeze me out of my desktop programme as I use it so much.
I have not yet found a way to contact Adobe should that need arise - the links on my Photoshop support programme don't take me anywhere
It worked fine on first try to the new laptop.
The store obviously did the right thing for me!