Every app in GAPPS works fine except Google Play Store and Google Play Services. How to fix them? I've done the factory reset, yet I see the  popups  "Unfortunately Google Play Services has stopped". I've  tried reinstalling the GAPPS but a weird situation came up.  I can sign in but the pop up Google play has stopped kept bugging. Plus every app under GAPPS works fine except for the Google Play Store which I cannot connect although I've signed in into my Google Account. 

The two apps (Google Play Store and Google Play Services) has troubling me so much.  I've tried  reinstalling, clearing Cache, factory reset, and I can't find the button to uninstall updates for these two preferences. I've tried dozens of APKs, and various versions. I'm using the Lenovo Vibe Shot Z90-7 with Android  5.0.2, running on Vibe UI V2.5.
I installed a GMS Core(Google Play Services) version 7.5.71(1955121-448) apk.

I'm using Google play ver 3.1.11 (2044178-836)

This worked for me.