How long ago and where did you purchase it from?
The issue is that Photoshop 5.5 is extremely old so I am not sure if Adobe would reissue a new product key for you. Newer products have the ability to have new product keys reissued if they are lost or need to be replaced.
Please call 1-***-***-**** to see if they can reissue the product key for you.
If you can take a minute and use the rating system to rate our session as EXCELLENT, GOOD, or OK and press Submit so I am credited with helping you.