To get the latest compatible for an device running Android 5.1.1 (Lollipop) , you should target version 35.2.19 or similar releases that still support API 21. While Google officially ended system updates for Lollipop years ago, you can still manually update the store app using a trusted APK. Direct Download & Installation
If the installation fails, it usually means you downloaded an APK meant for a newer version of Android (like Android 7.0+). Go back to the download site and look for a slightly older version of the Play Store that specifically lists Android 5.0+ support.
No. Material You (dynamic color) requires Android 12+. You will get the classic Material Design 1.0 interface, but with updated backend features.
: Use your device's browser to visit one of the trusted sites above and download the version for Android 5.0+.