Android 5.0 is a big step up in security with its tweaked implementation of SELinux. Chainfire managed to get root on Lollipop shortly after it was released, of course, but the process has been a little more messy. There are also a fair number of root apps that are broken on Android 5.0. The newest build of SuperSU from Chainfire might fix many of those issues, though.
If you're interested in trying the SuperSU v2.23 BETA, you can grab it from Chainfire's site. Chainfire is looking for feedback on any root apps that were previously busted on Lollipop which may now be working with the beta. You can post such things in the XDA thread. He hopes to have this version added to the Play Store in a few days if testing goes well.
The SuperSU beta is a standard TWRP flashable ZIP, so it's nothing too exotic. You will still need a patched CFAR kernel to enable SuperSU on Lollipop, but you only need to do that once. As usual, proceed with caution, beta software, flashing, blah, blah, blah.