The 5D3 is indeed a very good camera. I even do use it more then the 1Dx.
Basic sports and wildlife can easily be done with the 5D3. It has a very good and reliable AF. And of course it's FF, which will give you high IQ photos.
However, I even did order a 7D2 for using next to those cameras. When speed is really important then you will find the 6fps of the 5D3 low compared to the 12fps of the 1Dx. So having a good backup solution if any of those cameras would fail, I ordered the 7D2.
If I only would buy ONE camera then it would be the 5D3, as this is a very nice general purpose camera.