Install a fully functional Audible app on Android older than Android 6.0

I just bought a Samsung Galaxy S5 Mini, featuring Android 5.1. However, I cannot install the "Audible" audiobook app via Google Play (no search results). I know that this should work, as I have the exact same device (bought earlier) where Audible is running (automatic app updates are switched off) I tried downloading an older version (Audible-2.16.1) from www.apkmirror.com (not sure if the website is trustworthy) and installed it manually using ADB and USB debugging. The app kind of worked. At least I could log in and see my audiobooks. However, when trying to download any of the books, I get error messages. I assume that the app tries to connect to the wrong (old) server when downloading. Does anybody else have similar problems and knows how to get Audible going on older devices?