I think I'm preaching to the choir here
Hopefully I'm helping jmark.
From an instructive point of view: There are (at least) two ways to look at it.
1) Consider the sample space. It consists of every possible outcome when you toss 5 dice. Each outcome has equal probability and the probability of each single outcome is 1/6^5. Now using the rule of sum simply add up the probability of all the outcomes you're interested in. There are 10 outcomes that contain three 5's and two 6's. So the probability of getting three 5's and two 6's is 10/6^5. You can use counting techniques (combinations) to get the numerator but the key here is that you're adding up the probabilities of each outcome you're interested in.
2) Use combinations (counting techniques) to arrive at the probability of getting three 5's and two 6's when you roll five dice. In this method you count up the number of ways it's possible to get three 5's and two 6's. (i.e. 55566, 55656, 55665, etc.) Using fast counting this will be C(5,2) OR C(5,3) just as kittens pointed out. This is the number of outcomes of interest. To get the probability you divide that by the total number of ways anything could happen = 6^5. So, the probability is C(5,2)/6^5 = 10/6^5. In this case we didn't add up any probabilities - we computed the value of a fraction where the numerator is the number of outcomes we're interested in and the denominator is the total number of outcomes possible. No rule of sum.
When you think about more than one way and you get the same result, this is a strong indication you're thinking about it correctly in all cases.