Different sets of dates compared to a static number (Lame description, but I'm lost)

First off I'd like to apologized for the following description of my problem. I'll try to make describe as best I can. I work at a hotel and I make sure that every guest has a manager personally assigned to them during their stay. I look at the number arriving guests 3 days prior to arrival and assign the manager. The problem is that each manager needs to have a maximum of 5 guests but because we assign prior to arrival and each guest's stay varies in length, I can't keep track of how many have been assigned. So here's the question (I think), if I have a set of dates that looks like this
9/14/2013 9/18/2013
9/16/2013 9/21/2013
9/15/2013 9/20/2013
9/16/2013 9/20/2013
9/14/2013 9/15/2013
9/16/2013 9/23/2013
9/14/2013 9/17/2013
and today I'm assigning for the 17th, I can see that this manager will have 5 guests because there are 2 people departing on or before the 17th. What would the formula be to get a sum of guests that will be assigned to that manager on the 17th?

I really hope this makes at least a little sense. Please feel free to ask questions, I could be forgeting to explain something. THANK YOU SO MUCH!!!

So let's try it with SUMPRODUCT. Have a look at the example below:

SUMPRODUCT.xlsx

Ursul,I can't thank you enough for your help on this. It works perfectly! Thank you a million times!

Thanks for the feedback, please mark the Thread as 'Solved' and if you wouldn't mind, click on the "* Add Reputation" for me.

All the best, cheers