In addition to advice already given, use use the 5 fps with AF, still anticipating, pressing the shutter button a little ahead. You will have many shots to delete but that should leave you with a few good ones. Also, do not be tempted to zoom in too close, leave quite a border around the main subject, which will increase the chances of having all of the subject in frame.
Agreed, the ContinuousAF(with A/F between each frame) combined with A/F tracking might do a reasonable job. This is not to be confused with simple 'burst mode' which will only autofocus once at the beginning.
I suspect this combination is best used in manual or P mode.
That isn't quite correct. If you set the burst mode to 2af or 5af the camera will use AF with the exception that it will be the focus from the first frame if the burst is taken while shooting video. pg 87 of the manual.
I took a number of 5af burst shots of the grand kids playing in a pool when I first got the camera and the results for focus were quite good. I am sure using the 5af burst mode by the op would help him get some good shots. I was amazed at how far from start to finish they got within a second and many shots they ended up well outside the frame.