Possibly, but not guaranteed. Google’s auto-update mechanism on Lollipop is erratic. You may need to manually update every 6–12 months using this same method.

The Play Store requires Google Play Services to run. If your Play Services version is too old, the Store won't open. Ensure you update Play Services to a version compatible with Android 5.1.1 as well.

Tap on the APK file and select "Install." Android will update the existing Play Store app with the new version.

Your installed WebView is outdated. Update Android System WebView to version 119.x (last for Lollipop). Reboot.

Android 5.1.1 Lollipop remains a reliable operating system for many legacy devices, media players, and budget tablets. However, as the Android ecosystem evolves, older devices often face issues with pre-installed applications. System apps can become corrupted, or the built-in app market may stop updating automatically.

To ensure a smooth and secure experience:

To get the Google Play Store on Android 5.1.1:

Sign in with your Google account. If already signed in, everything should work faster and with fewer errors.

Follow this simple process to get the Play Store installed on your Android 5.1.1 device.

Install an appropriate, trusted app store as a temporary alternative

For Android 5.1.1 (API Level 22), you need a version specifically built for Android 5.0+