Rooting Android 5.0 Lollipop via ChainFire Auto-Root Tool

You can easily root all Google Nexus devices running Android 5.0 Lollipop with the ChainFire Auto-Root Tool.  You can find the download repository for each device HERE. A total of six Nexus devices can now be rooted using ChainFire’s one click auto-root tool.  Android 5.0 compatible CFARs are now available for the Nexus 5, Nexus 7 2012, Nexus 7 2013, Nexus 9, and Nexus 10, amongst others.  The only model not compatible is the Nexus 6, but we expect that it will come soon as will all Google Play Edition devices. 

All downloads contain .img files bootable through Fastboot.
Make sure your device is in Fastboot mode (you get there by holding VolUp+VolDown+Power when the device is turned off), then run the included script for your OS. On Linux and Mac, you may have to chmod +x root-linux/ before the script does anything.
A special boot image will load, which will install (only) SuperSU, then reboot into Android.
The included scripts perform an "OEM bootloader unlock". If this fails, the root will not work. If it succeeds, and you were not previously unlocked (first time rooting), it will probably wipe your data!  As I always say, please BACKUP!
For some device (Sony, Verizon, etc) you may need an OEM-specific tool to unlock the bootloader. Please do not forget to check and use this tool, if provided by your specific manufacturer.