Did you buy a Canon EF 500mm f/4.5L? (Not a zoom, but a lot of people use the term when they actually mean "telephoto".)
If so, when you add a 1.4X Teleconverter to it, the combo is an effective 700mm f/6.3.
70D is "f/5.6 limited", meaning that it's AF system will not be able to autofocus that combination.
But 5D Mark III is "f/8 capable" and should be able to autofocus the combo. However, this feature is limited to one or a few of the AF points at the center of the array. Check your user manual for more info.
Also search the internet for info about taping up some of the contacts on the teleconverter, so that it's "hidden" from the camera. After doing that, you should be able to get the combo to autofocus on both the 70D and with all the points of the 5D Mark III. AF might be a bit slower and may hunt at times, especially in lower light or lower contrast situations. But it should work.
The only down side to the tape trick is that the EXIF metadata willl show the focal length of the lens alone (500mm in this case), because the camera doesn't "know" the teleconverter is there.
EDIT: I just noticed the EF 500mm f/4.5L isn't on the 1.4X III compatibility list (see above). Not sure if it was just omitted because it's a fairly old lens, or if there is actually an incompatibility between the old lens and the latest-and-greatest teleconverter. If there's a problem, you might try a Kenko 1.4X instead... Ther're pretty close to the image quality of the Canon and considerably less expensive. The cheaper Kenko "MC-4" 1.4X is sharp in the center, but less so in the corners... so might be a good choice to use on an APS-C camera like your 70D. But on the full frame 5DIII, you might prefer the slighlty higher priced Kenko "Pro 300" 1.4X, which has better edge to edge, corner to corner sharpness.
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Alan Myers
San Jose, Calif., USA
"Walk softly and carry a big lens."
GEAR: 5DII, 7DII (x2), 7D(x2) some other cameras, various lenses & accessories
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