I keep regular old mozzarella cheese sticks in the fridge. 5-yo is able to help himself to those, which is helpful when I'm in the shower and he is "starving." He also snacks on Applegate farm salami and grass-fed hotdogs. He also likes bananas. He used to eat walnuts, but not right now. Apples come and go with him. He drinks a lot of milk, which is a snack in my book. It's not a big menu, and not super-duper-optimal, but it works for us, so that's where we are.
I don't really limit his carbs other than not making a "starch" with dinner and keeping sugar out of the house as much as possible. He's growing.