Why....

could be that residents of other houses take all the food and your deceased had problems getting any for their house(s)

so even thought you technically have enough food for everyone, when the people stop by the warehouse they take enough to fully stock their homes and leave nothing for others

i have found i have to surplus alot of food just to make sure everyone eats

This indicator count only things in stocks. Items in houses are not counted.

Some possibilities

(1) "death march" which from what I've read the developer is supposed to have fixed, but maybe he only alleviated it and there are still ways it can happen. Is there a stream, with no bridge across, that comes not from off the map but from a spring near the edge of the map so that people can walk round the head of it?

(2) trapped against a river bank by a newly-completed building. I've seen this in a playthrough video - a child out playing, walked through a construction site to the edge of the river - which wasn't straight; the building when completed blocked the way out. The trapped child, unable to reach home, starved.

(3) food in wrong place. People only eat food they cook at home (except homeless people cook at the storage cart/barn/market). I believe when running low on food at home they go shopping at the local market, if there is one, otherwise at the nearest barn (unless that has no food at all). So if the 5011 food is 5000 in one barn (e.g. in what we call a forest hub) and 11 in another (e.g. next a fishing dock) then people living near the latter could run short. Because they go for the small amount nearby, even if insufficient, instead of for the plentitude further away.

Note - 4 or 5 food's-worth is an average catch for uneducated fishermen, whereas it takes 12 or more to give one person, even a child, a square meal.

5000 food should be plenty for 32 citizens, but why so few nearing the end of the 19th year?

There are things about Banished that exasperate me, but starvation isn't one of them.

How about you tell us what is going on in your town. Next time the "people are starving" icon shows in general statistics, click it to see who, where and what they are doing. From each person's display, click house icon to see where they live, then the house's inventory tab to see what food it has. If it seems short, go through the other people in the house to see who (if anyone) is going shopping, with what result.

Having a well-stocked storage barn near homes is great...but it won't matter if a lot of the people living in those homes are working far away from them. (I explained more in my reply in the other thread before I saw this one.)

Also, markets do nothing for distribution, per se. Market vendors actually only gather food from storage barns (and, to a much smaller extent, stockpiles) and take it back to the market; townsfolk still have to visit the market -- just as they would a storage barn -- and carry supplies home themselves. And the more workers you've assigned as vendors, the more food is siphoned out of these local storehouses and into the market...which, even if it's centrally located (which it had better be, if you've only got one), is still going to mean that people on the outskirts of your settlement are going to have to be walking a lot further than they should.

Doesn't the yellow circle around the market mean that people living outside the circle will use their local storehouse instead? Though I don't know how accurate the circle is if a house is well inside the market's circle, with a short journey between them going by the distance the deer swims, but an awful long walk round by bridge.

Where to put a market if you only have one? I'd say close to the blacksmith who needs iron fetched from distant stockpiles. And if the market can serve fishermen who'd otherwise be losing health from having nothing but fish in their diet, so much the better.

The only time that I've found this happening is when I've asked my citizens to harvest something and I've accidently clicked on an area on the 'wrong' side of a stream. The citizens walk so far out of their way trying to cross the head of the stream that they can't get back to a food source ie any house.

I think that's the radius within which that market's vendors will gather supplies from the primary storage facilities (or maybe just the area they'll prioritize gathering from?). I haven't paid close attention to whether citizens give any preference to market over storage barn, but I doubt it. I think when they need food, fuel, tools, etc., they just go to whatever the nearest place is that has that type of thing (the game's reckoning of "nearest", whatever that might mean ;P ). In fact, it would mean that markets are much worse than I had thought, if the game caused a household to visit a market half a mile away (within whose "service" radius the house falls) for food, ignoring an undepleted storage barn right next to their home. But I don't think it does.
As far as I can tell, the big danger with markets is that, unless you keep the number of vendors low, the market(s) can deplete all the warehouses very quickly (ones nearby, anyway), leading to too-long walks for people living further out from the former -- especially for those whose workplace is in the opposite direction.

And I'm not sure what the vendors' rules are regarding what to pick up for the market, but, in my experience, they won't go to any great trouble to gather stuff like firewood and raw materials -- they obviously gather some, but they mostly seem obsessed with food.

But I've just never really been great at using markets effectively, myself. My preference is for a collection of interconnected hamlets, each of which has its own food production and storage facilities, but which share other facilities where possible, with just enough housing built near permanent worksites that nobody (normally) has to walk too far. Markets don't really work very well in such a setup, in my opinion. But it's certainly possible that I'm misunderstanding something about them.

OMGi just rage quit because of this also! love the game but simple stuff that should work isnt....

OMG so much yes this is maddening. I have had 4 gathers in a row die of starvation with food on hand markets scattered around and storage barns all with food in them. I see the knife and fork and think what the hell there is food around, check the closest barn 25 eggs, 18 beans, 10 fish Hmmm maybe a little low, check the market close by a couple hundred of several crops. The gatherer says "looking for food" wanders way the hell out in the woods away from all of these no rivers nearby and starves. The replacement almost instantly also gets a knife and fork and again wanders out into the woods past a mushroom and starves, the 3rd replacement also immediately displays the knife and fork walks to a barn with food takes none wanders into the woods and starves. His replacement displays the knife and fork and I start screaming obcentities and rage quit. I suspect this had to do with them all moving into the same newly built house that only has firewood but for gods sake if they won't pick up the food from the storage barn next door what the hell am I supposed to do. If this was a crap game I just wouldn't play however it can be really fun until this crap happens.

It's really strange that so many people have started reporting this. To my knowledge the game hasn't changed in ages. Do you have a save game you can put somewhere that reproduces this problem, I'd like to take a look.

Unfortunately I don\t after calming down some I resumed playing so the save I have is several years later without that problem anymore. Instead new problems caused by me that at least I know or can figure out why. I will say I don't think I will ever build markets again any place I would have I put a storage barn and stockpile and in my latest game have had no problems. That doesn't mean anything really as I am not very good at the game but I will through it out there.

Warren