Crop yields vary vastly depending on soil conditions, amount of rainfall, fertilization, pest control, etc. On my family's farm, there are places where the wheat grows tall and thick, and less than 10 feet away, plants are so thin and sparse that it would almost be better to let that area go fallow.
In any case, crop yields for barley tend to range between 5 and 40 bushels per acre. Here in Colorado, that number is typically around 25 bushels/acre.
Converting this to pounds per square foot isn't exact - a bushel is a unit of volume. Healthy barley will be more dense than unhealthy barley, but farmers shoot for 48 pounds per bushel in barley harvests. Using that figure, you'd be looking at .027 pounds per square foot.
If you were doing this in your backyard, and were committing more resources (water, fertilizer, time) than what a typical farmer invests, you might be able to see twice that amount. This would mean that to harvest enough barley for a 5-gallon brew, you'd still need around 200 square feet of land.