You'd have to walk for hours to check all the prices and work out the cheapest from various supermarkets though. Also, the more calories you burn walking across town to find, purchase, and carry home the very cheapest food, the more you need to eat...
Five kilometers sounds like a very sane maximum distance for shopping, which is manageable in one hour (two hours round trip). You don’t have to visit every shop each day, as the prices will be roughly the same and you can note new ones as you get to the shop the next time. Walking requires nearly no energy, compared to the standard energy requirements of the human body.
Also note that a bicycle for as little as £20 can speed up transportation immensely at nearly no cost (of course, you might want to invest a further £3 in chain lube, but, well).
