Sorry to hear of your failure.
Regarding your question about restoring the files: No. You're going to need to install it and you're going to need to activate it. If you've used up your allowed two activations, you'll need to call Adobe Customer Support, explain to them that you've recovered from a computer failure, and they'll work their database magic to make it possible for you to activate your software on your new system.
Might not be a bad time to think about upgrading to Photoshop CC, since you're starting afresh. There are some substantial l improvements since Photoshop CS5, especially in the area of raw file conversion. And don't miss the $9.99/month deal.
Thanks for the encouraging answers.
I’ll follow your advice once I have a new Mac Pro to replace the one that died.
All the best,
I'm sure it'll work out okay.
By the way, if you're in a Creative Cloud program I don't think you'll need to call anyone. Just log in on the new machine.