I always knew mine and my mom's budget. I mean, not at like 5, but once I was around 11 I did. Heck when I was a teenager I handled all our grocery shopping and was often put in charge of paying bills. Not because my mom couldn't, but she worked full time and went to school and often picked up an extra job or extra shifts so we could make it, so she didn't have time to grocery shop or sit down and pay the bills. I also handled our laundry, made us dinners, and after seeing what she spent eating in her work cafeteria every day, started making her lunches. But our family dynamic was different then the average families, it was just the two of us, she had to rely on me to handle some adult things or she would've gone batty. And I liked it, I felt very grown up with my coupons and grocery list (as an adult I feel less grown up with my grocery list and can never remember the dang coupons). And I'll say this, I was much more prepared for adulthood then my friends were. I had to sit most of them down and go "Ok, so this is a budget"....and credit cards are not part of your budget.
However I think "No, we can't afford that", is a pretty basic standard thing most parents say to kids. "Mom, I want a iPad!", "No", "But why not?", "Because we can't afford an iPad", "But I want one!", "We still can't afford it", seems like a reasonable answer to me.