Might be late to the party here, but people are saying "where are the carbs" when that food list is mainly carbs (which isn't a problem).
Cheerios, carbs.
Apple, carbs.
Strawberries, low carb, mainly fibre and water, some carbs
Grapes, carbs
School dinner - balanced (will have protein and carbs, with limited added sugars due to guidelines at this age)
Chicken shapes - mainly protein but breaded - balanced
Beans - protein and carb, with a slight lean on carb - balanced.
Pretty low in added sugar - probably within the whole "6 lumps a day" thing which is kudos to you.
A 5 year old needs 1800 calories a day, and technically, should only have 20g of added sugars a day. Depending on what the school dinner was, you might be about right.
Kids will say they are hungry for a variety of reasons, including boredom, the fact that what they just ate was very yummy and they want more, the fact that what they ate was kinda meh and they want better, thirst, or genuine hunger.
Sometimes they will have a ridiculously hungry day, or hungry week, or hungry month, for no apparent reason (which usually ends up as a growth spurt) (or can end up with them just starting to look a bit round, depending on the child).
Personally I'd be interested to see if he was less hungry if you substituted the dinner for a small chicken breast or a couple of mini fillets, a small jacket potato or some new potatoes, and a reasonable volume of veg like broccoli/mange-tout/Mediterranean mix - for the same sort of calories I suspect he'd fare better due to the volume factor. But I get that it can be difficult at this kind of age to get success with that kind of mix. You kind of build up to it by around 7 or 8...