Android 5.1.1 remains a popular OS for vintage Samsung Galaxy tablets, older Nexus devices, and budget smartphones. However, because this version of Android is now several generations old, you must be specific about which version of the Play Store you install to ensure compatibility and security. Why You Might Need a Play Store APK for Android 5.1.1
If you want to be 100% sure your downloaded file is authentic and the possible: Android 5
It sounds like you're asking for a that would make an APK download source for "Google Play Store for Android 5.1" the "best verified" option. older Nexus devices
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