No. The standard APK installation method works on all non-rooted Android 5.1.1 devices.
The following papers provide comprehensive insights into APK downloads, installation security, and market evolution relevant to that timeframe: Top Research Papers on Play Store & APKs google play store apk download for android 51 1 top
Once downloaded:
: Sites like APKMirror and OldVersion maintain archives of these specific builds for legacy device maintenance. Google Play Store (Android 5.0+) APKs - APKMirror google play store apk download for android 51 1 top