In YNAB, you enter all of your spending as it happens, be it cash, credit, debit, checking. They also have apps for phones, so you can do it when you are out and sync later at home. You can make a habit of recording yor spending every night, or if it works for you, every week. fwiw, my checking and my credit cards also have downloadable files that open into ynab and can import all your data. its pretty easy.
I find its easier to stay in food budget if I have a menu plan, and therefore, a grocery list.
You *could* take over grocery shopping as a gift to spouse and then you can control spending there.
also, in ynab, on the app and in the program, when you pull up a category, it tells you how much is left in the category to spend.
but mint is also good to show you past spending and easily see trends. I use both.
For 5 people food-wise, Id think you could get down to at least 150 per week. maybe lower, depending on how good your frugality muscles are and if you eat meat or buy coffee/alcohol, etc.