Thanks Neuro, I did indeed check the menu for beep function function and I made sure the 5D3 was not in servo mode. I should have mentioned that in my initial post!
I will probably just live without the beep. It wasn't very loud anyway and if there was much background noise I often couldn't hear it. An adjustable volume beep would be nice in some future body.
I suppose I could try resetting all functions and see if that restores the beep, but then I'd have to restore all my personal settings and that seems like too much work.