ok kids solved.-Go to Settings->Applications->Manage Applications->All
-Select "Clear Data" for Google Play Services and Google Service Framework
-Reboot the deviceGoto browser and search Google Play Serivces. click the link to the store. and click update
Suddenly I checked this link https://www.androidpit.com/install-google-play-services-apk and downloaded the APK that was pointed out for my PC e.g. Android version 5.1, X86 CPU and 'non specified DPI.
Now it is rock'n roll for me. Google Play services was updated and Google Play store works just fine.
Remix OS for PC is of course, as many have said many times, but it works pretty stable for me know and it fun to have Android in a PC. So far I have only installed instagram, Droxbox and a few more, but this looks good for a start....
/putte
http://liliputing.com/2016/01/remix-os-for-pc-how-to-install-the-google-play-store.html