I use a few distribution groups with my Exchange Online-hosted personal email. I delegate myself the ability to send as these groups so that I can send from other email addresses without having to have other mailboxes.
Recently, when when setting up a few distribution lists, I ran into this error when sending as them:
Your message did not reach some or all of the intended recipients.
Subject: test 123
Sent: 4/2/2016 8:09 PM
The following recipient(s) cannot be reached:
nonesuch on 4/2/2016 8:09
This message could not be sent. Try sending the message again later, or contact your network administrator. You do not have the permission to send the message on behalf of the specified user. Error is [0x80070005-0x0004dc-0x000524].
This was in spite of me having permission to do so. A quick Google search led to this Microsoft forum post. At the very bottom user SteveLindsey states that this error occurs when the distribution lists are hidden. Sure enough, when I unhid the distribution lists from the GAL, I was immediately able to send these emails. SteveLindsey claims that this is a known issue by Microsoft, though I was unable to find a KB during my brief search.
At the time of this post, I am not certain if this is specific to Exchange Online/Office365 or Exchange 2013 in general.