Before you rush to download, let’s identify the symptoms that suggest a manual update is necessary:

CNET How To - Install the Google Play store on any Android device

When you perform a "Google Play Store APK download for Android 5.1," you are manually downloading the latest version of the Play Store that is still compatible with your older OS. Automatic updates may have stopped due to regional rollouts or device manufacturer delays, so manual installation gives you control.

Aptoide, HappyMod, or any site that asks for device admin permissions.