> five fingers. We instantly think 'five' without counting because we have internalized the appearance of five fingers.

Don't agree. Our visual quick recognition pattern is "ONE hand" which we then mentally translate as "I know that always means 5 fingers, unless there's an obvious clue to the contrary".

If you doubt this logic, try people's reaction times when offered a range of signals of between three and say eight fingers. I believe the reaction time on three or fewer is much quicker, suggesting a short-cut that is different to managing larger numbers.