I do have adobe .CS5 PRODUCTION PREMIUM it will work on my computer

As far as i know, Photoshop CS5 won’t install on any macOS after macOS Mojave 10.14 because even though the Photoshop CS5 application itself is 64 bit Intel, included components like the installer are 32 bit that Apple no longer supports on macOS since macOS Catalina 10.15.

The same applies for the rest of the applications included in CS5 Production Premium.

https://support.apple.com/en-us/103076

Unfortunately, since most of the time a Mac won’t accept an install of a macOS older than the OS it shipped with, you won’t be able to install macOS Mojave 10.14 on your Mac mini. Besides i don’t believe there was ever a released to the public version of macOS Mojave 10.14 that would run natively on Apple Silicon processors.

 If you didn’t have any activation issues as mentioned by Conrad_C, then a Virtual macOS might work depending on how much free space your Mac’s ssd has, since you would need to install a complete macOS like Mojave or older.

It’s worth trying to install CS5, but there is a fair chance that some of it might not work. That version, CS5, came out about a decade before Apple started releasing Macs with Apple Silicon processors like your M2 Mac mini. So all the code in CS5 is for Intel processors.

macOS 26 still includes a Rosetta translation environment that can run software written for the old Intel Macs. However, there are more potential issues. Since CS5 was released 14 years ago, Apple progressively tightened the requirements for security, 64-bit compatibility, and more. The point is that because CS5 is so old, there are potentially many pieces of old code in there that might be rejected by current macOS. 

Adding to this, if you continue to upgrade macOS on that Mac mini, Apple has been warning everyone that future versions of macOS will drop compatibility for all Intel-based software (they’ll no longer include Rosetta). So even if you manage to successfully install CS5 on your Apple Silicon Mac mini today, its days are already numbered from the Apple point of view.

Another problem is that CS5 won’t know how to take advantage of the full power of your M2 Mac mini, such as GPU acceleration.

There may also be issues with online activation. If you run into this, see if the following link helps:

https://helpx.adobe.com/download-install/apps/troubleshoot/licensing-activation-issues/cant-activate-reinstall-legacy-apps.html

Yes I'm. The legal. Owner. Yes  I have serial number. Mac Mini. 2024. M2

​@joshuameyer 

Your second screenshot says it’s for macOS so it will not work on Windows.

Jane

​@joshuameyer are you the legal owner of the licence and do you have a serial number, also what operating system are you going to install it on, it will not install on a modern macOS.

Has it previously been installed on more than one computer.