Photoshop CS5.1 Crashing on Mojave 10.14.1

You can try the steps in this Macworld UK article. It specifically talks about solving a crash in Photoshop CS5 on Mojave.

https://www.macworld.co.uk/how-to/mac-software/open-apps-wont-work-mojave-photoshop-3684425/

But if that doesn't work, it will be difficult to troubleshoot. The code in CS5 is getting out of step with the many changes made to macOS in the 8 years since CS5 came out.

Photoshop CS5.1 is very old software and almost certainly not compatible with MacOS X Mojave.