The longer Android 5.0 is in the wild, the more we come across annoying little bugs. It sounds like Google might have broken something in the wireless framework in 5.0 because a sizeable number of users are reporting issues with connecting to their corporate networks after the 5.0 update.
Over the course of a few dozen posts on the AOSP issue tracker, users have narrowed the problem down to Cisco APs (which are quite common in business) running WPA2 with AES encryption. The device will ask for the password in order to connect, then it just goes to "Saved" and does not complete the connection. For people who have this problem, it occurs 100% of the time, but there are a few odd workarounds to avoid it.
Users have found that if you've previously set up the troublesome network on Android 4.4 (which doesn't have the bug), it will continue to work on Lollipop after a standard OTA. A freshly flashed device, or one that came with Lollipop seems to always exhibit the behavior. Likewise, updating to Android 5.0 via an OTA before setting up the troublesome network will prevent it from working. The report was started soon after the official release earlier this month, so hopefully someone at Google is working on it. 5.0.1 here we come.