Probably not - unless they are under 3oz and in your 3-1-1 bag. There are exemptions for babies and toddlers with regard to milk and formula but I doubt the TSA will consider a 5yo a toddler. Yogurt would be considered a gel as it can't hold its shape outside of the container.
You can bring other healthy snacks as long as they are not liquid or gel and purchase water after security to bring onboard.
You can check the website for your airport to see what vendors are in your boarding area. I have been pleasantly surprised lately at the choice of healthy foods offered, hopefully you will too.