Is your Android 5.1.1 device refusing to download new apps, or are you stuck with an outdated version of the Play Store?
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If your device is rooted, consider installing a custom ROM like LineageOS 14.1 (Android 7.1) for better app support. But if you’re stuck on 5.1.1, a manually updated Play Store keeps it usable for basic app updates. How to Download and Install Google Play Store