Finding groups of friends in social network data
Community Detection and Clique Percolation:

This is a community detection problem.  Here is a very detailed review article surveying the state of the art.

The Clique Percolation Method is also useful to explore as it pretty much solves what you may need to know.  You can also go through what Matching is, and link the concept with Blossom Algorithm. Though, this finds the maximum matching, you may slightly modify the algorithm to get the minimum matchings of 5 at least.