The 5D only works to f/5.6 however, I'm sure this lens will report f/5.6 to the body s all the other f/6.3 lenses do so yes, it will focus.
sure it does do AF , and body will show correct EXIF as 6.3 ( not sure how they fake the body to made body think the max aperture may be a 5.6 )
using with 600D no problem and i even can put a kenko 1.4 on it. although this time it cannot report correct exif (still F6.3 at tele) , but af are working.
tamron 150 600 with kenko TC are not working on 5D3 , reported as error 01. i've told tamron this issue and hope they can fix it ......
i am sure that this lens will perform better on aps cmos like 7D because more pixel count in same area and less vignetting (cropped)
also 1.6x we can have more reach (exposure metering and AF are challenged if the target is too small in viewfinder [as also on the metering and AF system] , sometimes APSC body does have advantages lol )

.Maybe MF first,then AF.

