Some Xiaomi phones are still available running the China build of MIUI ROM. Therefore, there are no single Google app installed on it. Luckily, its users can simple install Play Store manually either using third-part installer like Open Gapps or installing its .apk files.
Here in this page you can grab ready-to-use APK files of Gapps for Xiaomi Mi 5c, the newly released variant of Mi 5. The device is the most anticipated smartphone due to its processor. Instead of using Qualcomm Snapdragon or MediaTek Helio, Xiaomi has managed to develop their own chipset and planted it on Mi 5c. Meet Xiaomi Surge S1, a mobile chipset powered with Octa-core (4×2.2 GHz Cortex-A53 & 4×1.4 GHz Cortex-A53) processor and Mali-T860MP4 Graphic Processing Unit. More over, the phone also features 3GB of RAM and 64GB internal flash storage.
How to install Play Store on Mi 5c? Simply download the Gapps package, extract to get the .apk files, and install them one by one following this order:
1- Google Service Framework
2- Google Account Manager
3- Google Play Services
4- Google Play Store
5- Google Contacts
6- Google Calendar
Finally, do not forget to open Security app then choose Google Play Services and Google Play Store and allow / grant permission for all of its services.
No need of TWRP custom recovery, no need to root, just grab the APKs and install them accordingly.
p.s: This Gapp package is for Mi 5c running MIUI 8 based on Android 6 Marshmallow.
In this pack: Google Play Store v6.9.21.G-all  3270725.apk
Also read: Download Gapps and Play Store for Android Nougat.