The issue usually relates the depth of thread on the recorder. If it is too shallow, then the thread from our mount will not fully tighten onto the H5. The thread is a 1/4"-BSW standard, and you should always have the same depth, as the diameter. So approx. 6.0mm deep of thread. Some recorders don't do this, instead they make a very shallow thread. If you check the this may be the case.
The only solution would be to fit a washer or washers between the recorder & the mount. If you require me to send a couple of M6 washers I would happily do so for you to try. Let me know.
With the washer, I'd recommend removing the brass screw thread thumb wheel from the top bar. Fit the washer under the bar, and fitting the screw back through the bar. This would mean the thread is made shorter, but the recorder still rests on the rubber grip.