A LibraryLink library compiled with headers having a certain WolframLibraryVersion will not work with Mathematica versions that support only earlier WolframLibraryVersions.
For example, a library compiled with M12.0 (WolframLibraryVersion == 5) will work not only in 12.0 but also in 12.1–13.0 (WolframLibraryVersion == 6). However, it will not work in 11.3 (WolframLibraryVersion == 4).
Which Mathematica versions use which WolframLibraryVersion?