Imagine a game with two players who each throw 5 dice and only they can see their own dice. If we roll and I see that I have 3 sixes, what are the probabilities that there are at least 5 sixes in total (all 10 dice P(X>=5))? I believe this is a cumulative binomial distribution, but I can't figure out how to calculate the conditional. 

P.S. I'm not asking for the probability that the other player has 2 sixes, but the probability, given that I have 3 sixes, that there are 5 in total.