I think the answer
you are looking for is 5,000. But I don't agree with you about the between/among rule.
I'll quote the
Merriam-Webster's examples here.
There is a persistent but unfounded notion that between can be
used only of two items and that among must be used for more than two. Between has been used of more than two since Old
English; it is especially appropriate to denote a one-to-one relationship, regardless of the number of items. It can be used
when the number is unspecified <economic cooperation between nations>, when more than two are enumerated <between
you and me and the lamppost> <partitioned between Austria, Prussia, and Russia -- Nathaniel Benchley>, and even when
only one item is mentioned (but repetition is implied) <pausing between every sentence to rap the floor -- George
Eliot>. Among is more appropriate where the emphasis is on distribution rather than individual relationships
<discontent among the peasants>. When among is automatically chosen for more than two, English idiom may be strained
<a worthy book that nevertheless falls among many stools -- John Simon> <the author alternates among mod slang,
clichés and quotes from literary giants -- A. H. Johnston>.
I'm not looking for a logomachy
though. Grammar isn't absolute and it was a good riddle!