Do you live on rice and beans? That sounds like you're trading enjoyment for money. We (2 adults) spend about US$150 a week on groceries, and still eat out about once a week. Those groceries include three meals a day, with the leftovers of the night before being taken for lunch the next day. How on earth do people eat healthily and only spend $5 a day?
Carbs and fat are both cheap, and protein can be in the form of chicken and eggs. Vegetables are kinda expensive so I go with mostly broccoli, cabbage, and stuff from the Asian supermarket.
As for groceries, things like hygiene and cleaning products bring up total "grocery" bill, but $5 a day is very possible if it's pure food expenditure.
German groceries are quite cheap actually. When I visited, I bought a kg of sauerkraut for 1 euro and a liter of soy milk for 1.5.
My family of 3 spends around 100 to 130 Euros per week on groceries. We don't really are trying to save on groceries and usually buy what we want. We eat not much meat and usually cook fresh instead of using convenience food. We try to buy medium to high quality, local and seasonal food. So it's a tad more than 150€ per person but not that much.