Welcome to the forum.
First, a few questions:
1. Did you Deactivate Ps, prior to the crash - assume that you did not.
a. How many installations did you have for that program?
b. How many Activations did you have for that program?
2. Do you have either the physical media, or the download installer file?
3. Do you have your S/N, probably sent via e-mail, from Adobe?
If you have the physical media, and you have not reached the number of installations, or Activations, then you should just insert that, and if you have AutoRun ON for your multi-drive, just follow the prompts. If AutoRun is OFF, just navigate the disc to the executable file, and follow the prompts.
If you have the downloaded installer file (same installation and Activation caveats apply), Extract that, with the full folder structure, if it's a ZIP, or 7Z file, then in the Extracted files, click on the executable.
If you have exceeded either the number of installations, or Activations, you will need to contact Adobe Customer Support, as only they can reset either installations, or Activations. Even if you have not exceeded those limits, but did not Deactivate on the crashed HDD, I would contact Adobe C/S anyway, to get them to reset the Activations, in case this ever happens again.