Might I suggest the following:
First, look at the two cutting lips on your selected tapping drill. Use a magnifying glass if necessary, or even attempt to measure them. Recently I drilled a 4.3mm hole which turned out to be about 4.7mm diiameter and on inspection, the cutting lips were easily seen to be noticeably unequal.
Second, drill a hole in a piece of scrap material using whichever tapping drill you wish to use.
Third, measure the diameter of the hole so produced.
Now, measuring the hole is an almost impossible task so what I would suggest is that you use the shanks of a set of metric drills rising by 0.1mm until you find one which does not enter the hole. With luck, this will be 0.1mm above your chosen tapping drill, and hopefully the 5.6mm shank. You can always then measure the diameter of the shank to determine the exact size of the shank. This isn't an exact method, but given the difficulty of determining small diameters will get you somewhere in the correct region.
In the instance I briefly described above, the lips were obviously uneven, so no real need to measure, but I did and discovered how far out the drill was, so it wasn't surprising that my (5mm in my case) tapped holes were almost non-existant. Careful resharpening of the 4.3mm drill produced equal lips, a hole which would not allow a 4.4mm drill to enter, and a correctly tapped hole.
Good luck,
Peter G. Shaw