Chainfire's SuperSU root app receives a major update, now fully supports Android 5.0 Lollipop
SuperSU v2.35 is a substantial improvement of the app for several reasons. The most important one is the app's now fully compatible with Android 5.0 Lollipop. Chainfire reveals that it has been quite hard to find a viable workaround for hopping over the hurdles that Google has implemented in SELinux, along with everything else that prevented SuperSU from gaining root access. However, the app might still have issues with some of the early unofficial Lollipop builds that have surfaced for select Android warriors of late.
You can either wait for SuperSU to automatically update over the air or directly head to the dedicated download page and manually get the root-centric app.
Download: SuperSU (Android)