Ok, crunching some hypothetical numbers here...
$600/day for 5 days averages out to $120/day. Let's say you assign $25/day/person to each of the "real" adults. That leaves you $17.50/day for each of the four kids. Your 10yo will only have to pay adult prices if you go to buffets or all-you-can-eat places. At any counter service or regular sit-down restaurant, she'll be allowed to order off the kids' menu.
I think this is doable, if you're careful. Assuming we're not counting the cost of in-room breakfast groceries in your total, you can definitely do it if you don't have to have a table service meal every day. You could probably have a couple of them, if you're willing to eat counter service all the other meals. You just have to average $120/day. Some days you can go higher, and when you eat only counter service in a day, you'll probably be lower. Order ice waters for everybody at every meal, share desserts and appetizers if you want them. Bring snacks from home (crackers, fruit rollups, etc.) that you can carry with you instead of buying snacks in the parks.
It's doable. Of course, another option, if you don't want to have to watch every penny on your food budget, would be to go for 2 rooms at a value resort, which would free up a lot more funds. You could probably even afford to do the dining plan that way, but assuming you'd rather stay at the nicer resort and spend less on food, you can do it if you're very careful.