Hi graw, thanks a lot for your detailed response!!
The link to TWRP you posted was a life-saver ... the touchscreen in TWRP finally worked, and so, after wiping and rebooting, my Mi5 finally started MIUI8.6- awesome after a series of sleepless nights! I'm an amateur, but got kinda used to flashing phones (Nexus, HTC, OnePlus,..) but never had such difficulties as I have with the Xiaomi Mi5 with all the different versions of soft- and even hardware as it seems.
I'm risking going little bit off-topic here, but actually, my initial intention was to install CM13 after TWRP. May I ask for another tip in here, because when I try to flash CM13 from TWRP, I get "Can't install this package on top of incompatible data. Please try another package or run a factory reset.
Updater process ended with ERROR: 7
Error installing zip file '/sdcard/cm-13.0-20160521.zip"
(I was too scared to wipe data too ... wouldn't that also wipe the cm-13.0.zip I've pushed onto the device, preventing me from flashing it afterwards?)
Can you or anyone else give me a hint what to do in order to finally be able to use CM13 on my Mi5?