Assuming you have the correct .dmg file, installation is straightforward on older OS versions.
Step 1: Uninstall newer versions. You cannot run Kontakt 5.6.6 alongside Kontakt 6 in standalone mode easily. Use Native Access to remove modern versions first.
Step 2: Mount the DMG and run Kontakt 5.6.6.pkg.
Step 3: Choose your plugin formats (AU, VST, AAX). Pro Tools users: 5.6.6 works perfectly with AAX on Pro Tools 11 and 12.
Step 4: Run Native Access (older version) to authorize the library path.
Troubleshooting the "Library Not Showing" Issue: If you add a third-party library and it doesn't appear in the browser:
To understand the value of Kontakt 5.6.6, we need to look at the timeline. Native Instruments released Kontakt 5 in 2011. By 2016–2017, version 5.6.6 arrived as a maintenance update.
What changed in 5.6.6?
For many users, Kontakt 5.6.6 represents the last truly "lightweight" version before Kontakt 6 introduced Wavetable synthesis and a heavier GUI, and before Kontakt 7 introduced the new browser and HiDPI overhaul.
If you need macOS 11+ (Big Sur/Monterey/Ventura/Sonoma) or Apple Silicon:
This was one of the first versions to properly support macOS's native "Full Screen" window management (the green traffic light button behavior).