Easy way: Subscribe to GIS provider.
Hard way:
You need to condense each zip code to a point and get the latitude and longitude for that point. I would imagine that the US Postal Service uses the Post Office responsible for each zip code for this purpose.
For each address in your database, calculate the difference (in degrees)for latitude and longitude between the point value for that addresses zip code and the "center" of you search.
Convert the degrees to distance.
Apply Pathagorean therom to get radius.
If the radius is less than 15 miles you've got one.
This will get you people that live in a zip code with a center point less than 15 miles from the center point of the target. Not exactly what you asked for, but reasonably close.
