Lunch near the zoo with a 5 year old
How about Open City in Woodley Park? I see kids there all the time and they even have a kid's menu with crayons. You can sit outside as well if it's nice out.
For the adults it's pretty solid diner type food (roast chicken, tuna melts, omelets, pizza, ribs, meatloaf etc)
If the kid is into Asian food there is always Spices up near Cleveland Park and there is an Alero there for Mexican food.