I bought Photoshop CS5 a few years ago but after a recent reinstall

Try among the following:

To locate the serial number:

----------------------------

http://helpx.adobe.com/x-productkb/global/find-serial-number.html

http://helpx.adobe.com/x-productkb/policy-pricing/activation-deactivation-products.html

Error "The serial number is not valid for this product" | Creative Suite
http://helpx.adobe.com/creative-suite/kb/error-serial-number-valid-product.html

If all else fails, you need to contact Adobe Support either by chat or via phone when you have serial number and activation issues.

Here is a link to a page with options to help make contact:

http://www.adobe.com/support/download-install/supportinfo/