Develop classification model, given the k nearest neighbors I have a data set listing attributes of clients - a combination of ordinal, categorical and interval data. I am also given the 5 nearest neighbors within the data set for and have to essentially reverse engineer an algorithm for the nearest neighbors.

Given the complexity of the data I'm quite lost as to how I can work out and then obtain parameters of a distance function. I apologize in advance for the vagueness of the question but I'm not even sure where to begin.
If I understand you correctly, based on the data and the given nearest neighbors, you need to decide what distance calculation was used to determine the nearest neighbors.  It seems unlikely that you are being asked to create an altogether new distance measure, rather explore the different accepted distance measures.

If this is correct, it sounds like all you need to do is run the nearest neighbors recursively with different distance calculations and compare the results to the provided nearest neighbors to determine which measure created the 5 nearest neighbors you were given.