Janet,
If your site broke during the upgrade of the component, it's likely that you didn't update all of the modules as well. You can do so from the Joomla update manager. Once done, go to the JFBConnect Admin Overview page and make sure all of the versions are at v5.0.0 for modules and plugins that you have enabled.
Also, if you are using the JFBCSubscribe module, that has been discontinued and replaced by the JFBCFollow module. If you are using the JFBCSubscribe module, please uninstall it.
As for the Update Manager still showing that JFBConnect itself needs to be updated, please hit the "Purge Cache" and then "Refresh" button. That should make Joomla notice that JFBConnect has been updated outside of the update manager.
I hope that helps, but if not, let us know.
Thanks,
Alex