I have to ask a really dumb question -
WHY are you doing image deletion in camera? It's 1000 times easier to do it once it's all on my computer! If your concern is lack of space, then simply buy more memory cards. I'm using a pair of 16GB cards in my 5Diii set up just like the OP and get about 500+ shots on the CF card before it's full. I swap out BOTH cards at that point. Saves a LOT of time, hassle and 'pressure' in the heat of the moment.
For what it's worth, the first thing I do when I get home is to remove the cards from my camera and copy their contents to an appropriately named folder for the RAW and the JPGs. Then I put the 'other' pair of memory cards in the camera. If I had only used one pair of cards, I haven't deleted anything yet, thus, I have an instant backup copy in case I screw something up. If I took more than 500 or so shots and went to the second pair of cards, I copy that to the computer as well. Note that I do NOT format the cards in the camera until I am fully sure I have at least 3 copies of each photo, each on separate physical devices (SSD, HD, USB stick(s)). That way, I can delete what I want to and if there's an OOPS! (had 2 today, as a matter of fact), I can get it back from any of the other 2 copies.