No. The Play Store APK is signed by Google. You’re simply updating it manually, just like Google does automatically—except your method actually works.
A: Yes. The Play Store is a free app. Downloading the APK from a trusted mirror is legal and common for troubleshooting.
If your Android 5.1 phone is still slow, the problem isn't the Play Store – it's the lack of RAM or an old CPU. Here are two better alternatives:
: Open your "Downloads" folder, tap the APK file, and select Install .
How to Safely Download and Update Google Play Store for Android 5.1.1