@moskva I am not sure if I am qualified to suggest, since I am 5'10. But I can do 20 in a row, maybe more.
The way I achieved this:
- lost more weight (went from 15 reps at 70kg -> 20 reps at 65 kg)
- trained my grip strength
Pretty much it. Allowed to not only increase the number to 20, but also I do all 20 in a perfect form now. Before it was 10 in perfect form and 5 with slight swinging.
PS. Also, it is important to move not in a direct trajectory, but somewhat incline. When you pull up, you do not pull up to your forehead, but your chest, and when going down, you body is supposed to shift forward, slightly inclined from the vertical hanging. This is pretty tough at first, but when you master it, this technique gives you the edge.