Even though Photoshop CS5 is 64 bit itself, many of the included components like the installer are 32 bit.
Your specs show that the 2019 iMac has been updated to MacOS 15.3.1 Sequoia, so that being the case there is little chance Photoshop CS5 will even run on that even if you could get it installed and also activation of CS5 depends on a 32 bit component as well.
Migration from Time Machine is hit or miss with Adobe applications even on compatible operating systems, so many users end up reinstalling the already migrated applications to get them to work.
Since Adobe no longer will reset activations and you can't deactivate Photoshop CS5 on your crashed 2010 iMac, there's a possibility you won't be able to ever activate your Photoshop CS5.
I think your best bet if want to continue using Photoshop is to subscribe to the Adobe Creative Cloud Photography plan or check out Adobe Photoshop Elements 2025 and see if it meets your needs.
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