I have this problem with my emulator, i\'m using API 5.1.1 and i have the lastest version of Google Play Services from SDK Manager.
AndroidManifest.xml:
Since I haven't seen any working solutions in 2020. There are two ways to fix this:
Easy way is to create a new emulator with PlayStore Enabled
. Check before downloading system image for the emulator.
Hard way is to to install Google Play Store
on the emulator manually and make the update button work. You can refer to the installation part here.
After that, the app will automatically update the Google Play Services in a few minutes. That's all.
Note: If that doesn't work, Go to Chrome -> Search for Google Play Services and open the playStore link of that app and update it there.