Hello there,
If this is really Charliplexed (easy to prove) then with 5 lines there should be 20 LEDs, if they decided to use the maximum number.
I think the formula is:
LEDs=n^2-n
where n is the number of lines available, and LEDs is the maximum number of LEDs possible.
That is the maximum number of LEDs though and doesn't mean they all have to be there.
If there are 7+7+1 that's 15, but if there are 3 decimal points that would be 18 LEDs.
The drawing shows the maximum number of LEDs using 5 signal lines. Note each unbroken thick red line represents 2 LEDs each.
The above solves the problem of how many LEDs you can do with 'n' lines, but there is still one more problem to solve.
That is, how many LEDs can you DRIVE at the same time, and can you drive more than one at a time and still get even distribution of energy to each LED that has to be lit. Since you can not turn all LEDs on at the same time, you have to multiplex them, but the multiplex pattern and duration would have to be varied so that if you display some blanks like _ _ 1 which would be just 2 LEDs, and you display the most 1 8 8 you still want all LEDs to have the same brightness, and both patterns _ _ 1 and 1 8 8 to also have the same brightness. It would be strange to see that '1' light up super bright, and that "1 8 8" be somewhat dim. This would take a little more thought. This would also face the peak current per LED constraint, which of course has to be taken into account.