The major limitation appears to be the width of a print that can currently be printed which is 44".
http://www.largephotoprinting.com/ Maximum width = 44" by almost any length. From their site.
http://bigprintsusa.com/ Maximum width = 44" by a length of 72". From their site.
Your image file will need to be as perfect as humanly possible. Camera on a tripod, maximum resolution, ISO 100, lens at f8 or f11, mirror locked up, wireless remote to release the shutter, perfect exposure, perfect lighting and absolutely zero subject movement.
At the maximum resolution of your camera - 5184x3456 - by printing at 28dpi (dots per inch) the 3456 side would yield a 123.43'' long print and the 5184 side would yield a 185.1" wide print. Since the largest print width is 44" you'd need need 2 sections 44" wide and 1 section 32" wide. You'll also have to deal with losing a large amount of the 5184 side since to maintain the size you want you'll have to crop 5184 to 3456 (losing 1728 or 1/3 of the resolution) thus making your image file a square.
Be forewarned though that the results - even if you can get it printed - will be poor quality unless you plan on viewing your 10' x 10' print from about 150 to 200 feet. At 15 or 20 feet all you'll see is a horribly pixelated mess. Remember that billboards are usually printed at 20dpi and are viewed from 300 or more feet away as you're driving along at 55mph.
At your camera's maximum resolution a print made at a magazine quality 300dpi would be 11" x 17".