You can download the APK from these reputable community sources:

: Widely considered the most reputable source for verified APKs. You can filter specifically for versions that support "Android 5.0+" to ensure compatibility.

The latest version of the Google Play Store compatible with Android 5.1.1 (Lollipop) is version 22.3.27 (or older). However, please note that using an older version might not provide the latest features and security patches.

: Go to Settings > Security > Unknown Sources and enable it. This allows the installation of apps from sources other than the Play Store.