I think the farthest I have ever lived from a grocery store is maybe 2.5 miles... and that's when I was in college.
When I was a kit we had a grocery store on the other end of town, about 1.5 miles away, and a LOT of stores within a 15 mile trip.
My first job, I was in between a couple of groceries, the closest one being maybe 1.5-2 miles, if that.
When I moved to DC the closest grocery was literally across the street.
And now, where I am, I have 3 Giant foods (including the new one about a half mile away), 3 Safeways, a Whole Foods, an Aldis, a Lidl, 2 Super H Marts, Target, and Walmart within 5 miles.