I have Photoshop 10 on my personal laptop and have just gotten a new laptop. I have only used one of my licenses on that laptop, so should be able to load the license onto a second laptop. I downloaded the software from the Adobe site, but when I enter the serial number I am informed that it is not valid. I contacted support and they told me that it is an old version of Photoshop and that I need to purchase Photoshop 15. Unfortunately, this is only used for my personal family photography and it does not make financial sense to purchase such an expensive piece of software a second time. The person at support suggested that I use the forum to discuss as the experts here may be able to give advice. I am hopeful, but guessing you will just inform me to open my wallet.
Here's to hope!
We are only fellow users like you; so little we can do to make serial numbers work for older software not designed for modern operating systems.
If it is any consolation, Adobe has been running promotions during the holidays and through early January. On-line sites such as Amazon, Costco etc. maybe even cheaper.
It's even cheaper on Amazon at $60: https://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=photoshop+el ements+15
By the way, your application is Photoshop Elements (not Photoshop, which is much more expensive).