To manually update or install the Play Store on an older device, follow these steps using a trusted third-party repository like APKMirror :
Android 5.1.1 Lollipop is now considered a legacy OS. While stable, it no longer receives system-level updates from most manufacturers. However, Google still supports Play Store updates for Android 5.1.1 and up. To manually update or install the Play Store
Even with the latest version new, you might encounter hiccups. Here’s how to fix them: To manually update or install the Play Store