Best Tool to create a series of rings, and how to start, if possible

[SeanDonovan]

Hi,
I have a group of points, I want to create multiple rings that connect a maximum of five points at a time with the shortest distance possible between rings. They can be any type of rings, as long as they connect no more than five points at once. I was searching specifically ESRI ArcGIS tools and was having trouble finding the best tool for this job. I was wondering if anyone had a suggestion for a method or Tool to use that would make this task possible. Here is the group of Points I am working with. If this is possible. This is for a Fiber Network.
[ATTACH=CONFIG]28906[/ATTACH]

[DaleHoneycutt]

Take a look at the Calculate Distance Band from Neighbor Count tool or even the Generate Near Table tool.  My idea is that these tools can be used to calculate a buffer distance for each point.  If you have 3D Analyst, creating a TIN surface may be useful as the TIN will contain lines connecting the closest points (but not guaranteed to be 5 points).