If you have five consecutive men (or women) then the next person must be the opposite gender. In light of this you have to slightly adjust your analyses. You will then have to shift this and take into account that the tail (as opposed to the head of the line) just before (and after) must also be the opposite gender.
See if you can take the above into account to get a new answer.
Also if you meant to say "at least" so many people then disregard my response.