Did you upgrade your OSX in the meantime? Apple does not well run older software on newer OSX systems!
Unfortunatly, yes. So, do you think there is no solution?
the détail of error message is :
Dyld Error Message:
Library not loaded: @executable_path/../Frameworks/asneu.framework/versions/a/asneu
Referenced from: /Applications/Adobe Photoshop Lightroom 5.app/Contents/MacOS/Adobe Photoshop Lightroom 5
Reason: image not found
So can I find the file library?
I would suggest to look, if the latest version of LR5 support installing on the version you upgraded. As you don't give the versions you have, I cannot go and verify for you.
If your OS is not supported, then you are out of luck and you need to upgrade your LR to LR6. Fortunately for you, that is possible at little cost.
And please blame Apple for introducing incompatibilities and not Adobe. Microsoft with Windows ensures compatibility up to the highest level, and they even do not own the hardware.