Hi Andrew
I'm no expert but did a little research before I posted. Unless you fill the buffer in your camera (which I think holds maybe 15 RAW images) and need to fill it again before all the data has been written to the card, then the card write speed will not limit you. An example calculation: for 15 RAW files = 15x32 MB = 480 MB would take maybe half a minute to write to a Sandisk Ultra (where you may get a sustained write speed of 15 - 20 MB/sec). So unless you are taking more than 15 RAWs every half minute or so during the peak of your photography, you'll never be aware of any issues with this particular card. Of course, once a few RAW files have cleared from the camera buffer to the card, you can add more images to the camera's buffer. As such, you'll be able to take more photos within a few seconds of filling the buffer. Note, the speeds they quote on the front of these card are all read speeds (for the Ultra it is 48 MB/sec). Writing is considerably slower and usually not disclosed - it's necessary to look at online tests to find out how fast they actually write. Faster SD cards are available but more expensive (eg Sandisk Extreme). Similarly, fast CF card are also available but a lot more expensive again. The SD cards I'm referring to are SDHC. Not entirely sure what an SDXC card is.
Whether this option works for you will depend on the maximum rate at which you take photos - that will affect the type of card you need and how much you have to pay. In terms of brands to buy, I'd stick with the big names, eg Sandisk or Lexar but others may be in a better position to comment. I've never had a problem with any of my Sandisk cards. I use Ultra and Extreme versions: my RAW files are smaller (about 25 MB) but the buffer in my camera is a lot smaller and will only hold about 5 RAWs if I remember correctly.
Another thing I don't know anything about for your camera is the fact that it has both CF and SD slots. I don't know if the two can be used together and whether images can be transferred from one to another. That may open up further options and speed things up for you but those who own the 5D III could provide enlightenment on that.
Cheers
Glenn