Their numbers went:
1 - sesei
2 - sandi
3 - sinati
4 - fusese
5 - fakete
6 - faketi-tarosi-taure-sesei
7 - faketi-tarosi-taure-sandi
8 - faketi tarosi taure sinati
9 - faketi tarosi taure fusese
10- faketi tau tau
It helps to understand it when you learn that fakete (5) is hand.
6 is faketi-tarosi-taure-sesei = hand-one side-other side-one.
But other New Guinea Papuan language groups take the body-part tallying to extremes.
The Oksapmin developed a body-part counting system that went beyond one hand, up the arm to the head, and then down the other side. The Oksapmin example results in a numbering system of base 27.

They also had to memorise each of the 27 body-part names:
(1) tip^na, (2) tipnarip, (3) bum rip, (4) h^tdip, (5) h^th^ta, (6) dopa, (7) besa, (8) kir, (9) tow^t, (10) kata, (11) gwer, (12) nata, (13) kina, (14) aruma, (15) tan-kina, (16) tan-nata, (17) tan-gwer, (18) tan-kata, (19) tan-tow^t, (20) tan-kir, (21) tan-besa, (22) tan-dopa, (23) tan-tip^na, (24) tan-tipnarip, (25) tan-bum rip, (26) tan-h^tdip, (27) tan-h^th^ta.s
It's easier than it looks - you only have to go up one side, and then repeat the same names in reverse, down the other.
Most numbering systems started with finger-tallying, and the physical way this was done affects the number words that were derived from it.
When you get to 5, it's an open hand. In certain places around New Guinea, where this kind of finger-counting occurred, the words for number 5 should reflect just this.
Or six can be the little finger on the second, left hand.
In Gadsup, 6 = apä?tä?te mänayemänä?i - 1 added to 'weak hand'
In Bargam, the word for 5 is abainakinta (thumb-1); thumb is abainagin.
Fist should show up in many of the number words for 5, as well. (Trouble is, I don't know many Papuan languages, and not many travelling language recorders wrote down words for 'fist').I'll find the connections someday