5 miles is a long walk. That’s at least 1 hour and 15 minutes for a very fast walker, and probably around 2 hours for a more typical walker.

Plus you have to walk back, with groceries. Assuming you are feeding a family and not doing this 2-4 hour round trip every day, that means you’ll need a cart to push or pull.

Good luck pushing that loaded cart on a road with any amount of traffic. Most places in the U.S. where the grocery store is 5 miles away will involve either zero sidewalks and dangerous roads (more rural/suburban areas), or many many road crossings with lights that slow you down (denser areas).

I’m a big fan of walking. But 5 miles to a grocery store and then back is going to be way too much and too dangerous for most people.