Two suggestions:
1. Do a "Factory Reset" - you'll want to backup your data first, because it will wipe everything, but it will bring it back to "out of the box" condition, running Android 5 Lollipop. It's then pretty simple to restore everything if you have done a backup first.
2. If it's still sluggish, download the KitKat 4.4 Factory Image and restore that. You'll need the Android SDK on a Windows PC to manage the download and installation process.
Let us know how it goes - good luck.
(For the record - Android 5 Lollipop is working great on my Nexus 4 and Nexus 7 2013.)
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