I would think that running an unauthorized T-RackS 5 would only show the plug-ins that are available in T-RackS 5 Custom Shop ("TR5 CS"). Get the latest Authorization Manager here:
https://www.ikmultimedia.com/products/authorizationmanager/,
install it and Authorize TR5.
Start the Custom Shop program, login, go to the T-RackS 5 section and click [Gear] >> "Restore My Gear". You should then see your gear in TR5.
TR5 does not require CS to run - only to restore gear, try out new modules, etc.
The various TR5 downloads consists of 3 software products (T-RackS 5, the Custom Shop and the Authorization Manager) and a Serial Number. That Serial Number determines which gear is available, as standard, in the TR5 software. And, as you have found, the Authorization Manager (and Custom Shop?) programs may be old / incompatible versions. In my opinion, IK Multimedia should either:
-- update those download files so that the three programs are compatible
-- remove those 2 from those downloads and remind the user that they need to be downloaded too.
Just for clarification - I am not employed by, contracted to, or representing IK Multimedia.