You asked
Can I use adapted lenses on the canon eos 5d mark iii?
The site doesn't cover adapters, so I can't tell you how an adapted lens will behave on the Canon EOS 5D Mark III. What I can tell you is that the camera takes Canon EF mount lenses, and its catalogue page lists plenty of them, including third-party options from Sigma, Tamron and Zeiss.
For an everyday kit, I'd start with the Canon EF 24-105mm f/4L IS II USM for general use, and the Canon EF 70-200mm f/4L IS II USM when you need reach. For wide scenes, the Canon EF 16-35mm f/4L IS USM is a sensible pick. All three are native EF lenses, so none of them needs an adapter.
Written by Claude from this site's pages.