As the title says, I can't seem to get it working at all. I am running Android 5.0.1 on Nexus 5.
Since the AOSP did not have EAP-SIM support, there are different implementations on the market. [...]
Also, looking at the list of supported devices for EAP-SIM on this site, I didn't see any Google Nexus products, which might prove the statement on that answer.
Note: I would say that the list might be too localized and not too updated, so don't take it as a hard fact. Also, the answer was posted on Jan '14 (before Lollipop), so it might be outdated.
OTOH, it seems that Nexus 6 actually has this function, and Nexus 5 was supposed to also have it. However, Issue #81587 on AOSP Issue Tracker and Issue #509 on Lollipop developer preview might tell that Nexus 5 doesn't support EAP-SIM, even on 5.0.1 Lollipop.