It sounds like you're asking for a key feature that would make an APK download source for "Google Play Store for Android 5.1" the "best verified" option.
The search for “google play store apk download for android 51 1 best verified” ends at trusted platforms like APKMirror and APKCombo. Do not gamble with random websites. Use version 38.4.23 or 39.3.44, follow the installation steps carefully, and clear your cache. It sounds like you're asking for a key
Google Play Store APK Download for Android 5.1: A Comprehensive Guide Use version 38
Warning: Avoid popular but dangerous sites like rexdl, apkpure (old versions), happy mod, or androidapksfree. These often bundle adware or require dangerous permissions. Version: Google Play Store 42
Version: Google Play Store 42.9.16 (Latest compatible for Lollipop) File Size: ~45 MB Requires: Android 5.1.1 (Lollipop) – API 22
Issue: “Download pending” forever
Fix: Go to Settings → Accounts → Google → Remove your account and add it back.