Kid friendly in Union Square Area?
The kids will probably love Max Brener (B'way and 13th), which is a chocolate shop and restaurant. I find the food to be fine, and the tuna salad sandwich and caesar salad are actually pretty good. I think Heartland Brewery is probably fairly kid friendly and has some vegetarian options as well.
841 Broadway, New York, NY 10003
35 Union Square W, New York, NY 10003
Can I provide a non-recommendation? I've been to Stand burger a few times with my daughter, and though she's into eating fries, I've totally had enough of their uninspired burgers and indifferent service. Last time we were there, I spent the whole time wishing we were at Num Pang across the street http://www.numpangnyc.com/ (which is quite good, but may be more informal than what you're looking for).
Num Pang Sandwich Shop
21 E 12th St, New York, NY 10003
24 E 12th St, New York, NY 10003
You don't specify budget but Piola on 12th between University and B'way could be a good choice. Informal and inexpensive, there are plenty of vegetarian options (pizza, salads, pasta) and I think a 5-year old would love it. The pizza is good and while it's not competition for Keste or Motorino it is much roomier and less rushed. The staff is charming and friendly.
48 East 12th Street, New York, NY 10003