[Xiaomi Mi 5c Guides, News, & Discussion] usedbytes:
Here's a guide + script for installing SuperSU root on the Mi 5c.

I haven't yet managed to build a TWRP recovery image for it (I haven't really tried) - so this can be used to get root in the mean-time. (I also saw a Chinese TWRP ROM on the MIUI forums, but I haven't tried it myself)

Obviously modifying the phone system is risky, you may void the warranty, break it etc. I take no responsibility for that, and you use the instructions below at your own risk.

The script, and a few other tools I'm using for the Mi 5c can be found in my git repo: github.com/usedbytes/meri_tools

To use the script, you'll need a linux (or Mac, probably) computer with gcc and git installed, as well as a new-ish version of adb and fastboot. I'm running it on Arch Linux fine.

First get the phone into developer mode (tap on the MIUI version in About Phone 7 times), and enable adb debugging, and approve your computer to access debugging.

Then you need to download and extract the SuperSU "Installable Recovery" zip, and the Xiaomi stock ROM, which we will use for the install files.

Then, run the script below (meri_root.sh in the git repo).

The script installs all the bits needed, then reboots the phone with a rooted boot image. To make the root persistent, you need to flash the boot.supersu.img to the boot partition with fastboot (it just boots it by default).

#!/bin/bash
#
# Script to root the Xiaomi Mi 5c, by manually installing SuperSU
#
# Copyright 2017 Brian Starkey
#
# Permission is hereby granted, free of charge, to any person obtaining a
# copy of this software and associated documentation files (the "Software"),
# to deal in the Software without restriction, including without limitation
# the rights to use, copy, modify, merge, publish, distribute, sublicense,
# and/or sell copies of the Software, and to permit persons to whom the
# Software is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
# DEALINGS IN THE SOFTWARE.
#
# -- Disclaimer
#
# Obviously modifying your phone can be dangerous, void the warranty etc. etc.
# Use this script and the instructions within it at your own risk.
#
# -- Description
#
# The SuperSU installer seems to assume you already have root, and is intended
# to be run from a custom recovery (like TWRP). We don't have that, so we'll do
# some funny dances to do a systemless root without having root to begin with.
#
# The crux of the matter is using SuperSU's tools to patch the ramdisk and
# sepolciy (in /data/local/tmp, without root), then building a ramdisk with
# those components
#
# -- Usage
#
# Plug in the phone, make sure you have (persistent) adb debugging permissions
# and run this script like so:
# meri_root.sh SUPERSU_DIR ROM_DIR
# Where SUPERSU_DIR is a directory where you have downloaded and extracted the
# SuperSU "Recovery Flashable" zip file: http://www.supersu.com/download
# and ROM_DIR is a directory where you have downloaded and extracted the ROM
# from Xiaomi's download page: http://en.miui.com/download-322.html
#
# The script will make and boot a boot.img which enacts a systemless root.
# To make it persisent, you must flash it instead:
# fastboot flash boot.supersu.img
#
# By default, SuperSU removes dm-verity from /system and encryption from /data
# To prevent this, set PRESERVE_VERITY=1 before running the script:
# PRESERVE_VERITY=1 ./meri_root.sh ...

if [ $# -ne 2 ];
then
cat >&2 <<EOM
Usage: $(basename $0) SUPERSU_DIR ROM_DIR
Extract SuperSU zip file into SUPERSU_DIR, and the Xiaomi ROM into ROM_DIR,
then run this script.
EOM
exit 1
fi

SUPERSU_DIR=$1
echo ${SUPERSU_DIR}/arm64/su
if [ ! -f ${SUPERSU_DIR}/arm64/su ]
then
echo "Invalid SUPERSU_DIR" >&2
exit 1
fi

ROM_DIR=$2
if [ ! -f ${ROM_DIR}/boot.img ]
then
echo "Invalid ROM_DIR" >&2
exit 1
fi

# 1. Get mkbootimg and build it
git clone --depth 1 https://github.com/osm0sis/mkbootimg.git || exit 1
cd mkbootimg
make || ( cd .. && exit 1 )
cd ..

# 2. Copy the SuperSU binaries to the device
echo "Waiting for device..."
adb wait-for-usb-device
adb push ${SUPERSU_DIR}/arm64/*su* /data/local/tmp/ || exit 1
adb shell chmod +x /data/local/tmp/su*

# 3. Create the SuperSU systemless root image
# Ideally we'd set up security contexts too, but then you need to be running
# on an SELinux-enabled kernel in permissive mode.
# Instead, we will fix it on first boot.
dd if=/dev/zero bs=1M count=96 of=su.img
mkfs.ext4 su.img
mkdir mnt
sudo mount su.img mnt

sudo mkdir mnt/{bin,xbin,lib,etc,su.d}
sudo chmod 0751 mnt/bin
sudo chmod 0755 mnt/{xbin,lib,etc}
sudo chmod 0700 mnt/su.d

sudo cp ${SUPERSU_DIR}/arm64/{su,sukernel} mnt/bin/
sudo cp ${SUPERSU_DIR}/arm64/su mnt/bin/daemonsu
sudo cp ${SUPERSU_DIR}/arm64/supolicy mnt/bin/supolicy_wrapped
sudo ln -s /su/bin/su mnt/bin/supolicy
sudo chown root:root mnt/bin/{su,daemonsu,sukernel,supolicy_wrapped}
sudo chmod 0755 mnt/bin/{su,daemonsu,sukernel,supolicy_wrapped}

sudo cp ${SUPERSU_DIR}/arm64/libsupol.so mnt/lib/libsupol.so
sudo chown root:root mnt/lib/libsupol.so
sudo chmod 0644 mnt/lib/libsupol.so

# Run a script at first-boot to fix up the SELinux contexts on the image
# It will remove itself after running
sudo bash -c "cat > mnt/su.d/firstboot.rc" <<EOF
#/system/bin/sh
chcon -hR u:object_r:system_data_file:s0 /su /data/local/tmp/su.img
rm /su/su.d/firstboot.rc
sync
EOF
sudo chmod 0750 mnt/su.d/firstboot.rc

sync
sudo umount mnt

# 4. Copy the systemless root image to the device
adb push su.img /data/local/tmp/su.img

# 5. Extract boot.img
mkdir bootimg
mkbootimg/unpackbootimg -o bootimg -i ${ROM_DIR}/boot.img

# 6. Unzip the ramdisk
cat bootimg/boot.img-ramdisk.gz | gunzip > ramdisk

# 7. Copy the ramdisk to the device, for patching
adb push ramdisk /data/local/tmp

# 8. Patch sepolicy and the ramdisk, using the SuperSU tools we copied over
# earlier
adb shell "
cd /data/local/tmp
LD_LIBRARY_PATH=. ./supolicy --file /sepolicy ./sepolicy.patched
LD_LIBRARY_PATH=. ./sukernel --patch ./ramdisk ramdisk.patched
"

# 9. Pull back the patched files
adb pull /data/local/tmp/sepolicy.patched /data/local/tmp/ramdisk.patched .

# 10. Extract the patched ramdisk, and install the patched sepolicy into it
mkdir ramdir
cat ramdisk.patched | sudo cpio --no-absolute-filenames -D ramdir -i
sudo cp sepolicy.patched ramdir/sepolicy
sudo chown root:root ramdir/sepolicy
sudo chmod 0644 ramdir/sepolicy

# 11. Install the SuperSU init scripts
sudo mkdir ramdir/su
sudo chmod 755 ramdir/su
sudo cp ${SUPERSU_DIR}/common/launch_daemonsu.sh ramdir/sbin
sudo chmod 744 ramdir/sbin/launch_daemonsu.sh
sudo chown root:root ramdir/sbin/launch_daemonsu.sh
sudo cp ${SUPERSU_DIR}/common/init.supersu.rc ramdir
sudo chmod 750 ramdir/init.supersu.rc
sudo chown root:root ramdir/init.supersu.rc

# 12. Patch the initscript for our img location and set the su.img context
sudo sed -i 's;/data/su.img;/data/local/tmp/su.img;' ramdir/init.supersu.rc
sudo sed -i '\;on property:sukernel.mount=1;a\ \ \ \ restorecon /data/local/tmp/su.img' ramdir/init.supersu.rc
sudo bash -c "echo /data/local/tmp/su.img u:object_r:system_data_file:s0 >> ramdir/file_contexts"

# Optional: Preserve dm-verity on /system, encryption on /data
if [ ! -z "$PRESERVE_VERITY" ] && [ $PRESERVE_VERITY -ne 0 ]
then
echo "Preserving dm-verity"
mkdir ramdir-stock
cat ramdisk | sudo cpio --no-absolute-filenames -D ramdir-stock -i
sudo cp ramdir-stock/{fstab.song,verity_key} ramdir/
sudo rm -rf ramdir-stock
fi

# 13. Repack the ramdisk
cd ramdir
sudo find . ! -path . | sudo cpio -H newc -o | gzip > ../ramdisk.gz
cd ..

# 14. Repack the boot image
mkbootimg/mkbootimg \
--kernel bootimg/boot.img-zImage \
--ramdisk ramdisk.gz \
--cmdline "console=ttyS0,115200 earlyprintk=uart8250-32bit,0xF900B000 androidboot.hardware=song no_console_suspend debug user_debug=31 loglevel=8" \
--base 0x0 \
--pagesize 4096 \
--kernel_offset 0x0a080000 \
--ramdisk_offset 0x0c400000 \
--dt bootimg/boot.img-dtb \
--tags_offset 0xc200000 \
--os_version 0.0.0 \
--os_patch_level 0 \
--second_offset 0x00f00000 \
--hash sha256 \
--id \
-o boot.supersu.img

# 15. Boot it! (flash it if you want to make it persistent)
adb reboot-bootloader
fastboot boot boot.supersu.img
echo "Waiting for device..."
adb wait-for-usb-device