Is there any mechanism to delete images that were uploaded by members over 5 years ago, for example? My board is starting to consume more space than I'd like on my server, and I thought this could be a quick win.

There is no facility that would allow you to do this, no. You could potentially do topics, which would then delete the attachments with it, but thats the only method built in. The system won't allow items to be deleted that is attached to an item of content.