There are a couple of ways (requiring arcinfo license):
If the 5 points at each location have a common ID or attribute, you can run Dissolve using that ID/attribute to obtain mpoints, and then run Feature To Point tool to get a point from each mpoint feature.
If the 5 points within each cluster are spatially very close to each other and apart from other clusters, you can make a copy of the points using Copy Features tool and then run the Delete Identical tool. You should get one point at each location.