So it seems there's a plugin out there that Google installs on some computers that supersedes the one on their download page:
https://www.google.com/tools/dlpage/hangoutplugin

The one on their page gives you version 5.40.2.0. But most people are on 5.41.0.0 which seems like it should be the latest version except it's certainly not the one from their download page.

Does anyone have a version newer than that and know what the link is? I'm having a tough time triggering the prompt to have the newer version installed that some others seem to be getting.