Bad news. Can not run two different versions of the TSM/Spectrum Protect BA Client on the same Windows os.
No need to take my word for it. If you have a Windows test system, go and attempt to install the different version and see what happens.
Do realize that TSM BA Client 5.3.X does not support Windows 11.
You can attempt to install the 5.3.X client and see what happens.
If it works, that's great. If issues are encounter, don't call IBM Support because the tech will inform you that TSM BA Client 5.3.X is no longer support and it does not support Windows 11.
Good Luck,
Sias