You could use OpenGApps. I believe it is sanctioned by Google and allows you to easily select the latest version for your device architecture and Android version, customizing the package by which apps/services you want.
The Doogee X5 has a MTK6735 chip, which is 64-bit ARM. So you should select the ARM64 platform version and 5.1 Android version, and then decide which app package you want from there. Once downloaded, you can flash it via Recovery (recommended).
It is also possible to extract the apps for a manual upgrade. I just tried it this way on OSX (should also work on Linux):
Extract your downloaded zip file (to, for example, ~/gapps
)
Run the following commands:
cd ~/gapps/Core
lzip -d *.lz
find . -name *.tar | while read line; do tar -xvf $line; done
You'll now have some folders with the APK files. The ones of interest to you are probably:
gmscore-arm64/nodpi/priv-app/PrebuiltGmsCore/PrebuiltGmsCore.apk
gsfcore-all/nodpi/priv-app/GoogleServicesFramework/GoogleServicesFramework.apk