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hmm you might have to find the biggest land mass in map creation (most farm tiles) with as little water as possible. Have to pier to the 4 cornors of the map, and make sure all your housing blocks are manors. 200 in total
Which makes the progression
500, 1000, 1500, 2000, 3500.
So it makes sense to have the last be 5000. But I honestly can't think of any reasonable way to do it other than to go on peaceful mode, spend 20 hours building a kingdom of nothing but houses and city centers, and spamming festival to get up to the population and then having it starve out.
Even with 80% of all land area converted to farms in my own game, and all towns being on ocean/barren tiles, I struggle to sustain a population of 3200.
I thought someone might still be interested to see my findings so I've included everything down below.
=====================================================
Only essential buildings:
200 manors * 4 tiles = 800 manors tiles.
800 manors + (3 * 3 castle tiles) + (3 chamber of war tiles) = 812 manor, castle and CoW tiles.
(10 * 48) + (46 * 2) = 572 least amount of roads tiles.
1786 tiles within walls - 572 least amount of road tiles = 1424 tiles without manors, walls or roads.
29 food/orchard : 4 tiles/orchard = 7.25 food/tile.
5000 food : 7.25 = approximately 690 tiles required for orchards (none lost to exposure).
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Concluding, you could sustain an unhappy population of 5000 without immediately succumbing to hunger with approximately 734 tiles left. So, the achievement seems to be possible.
However, if you wanted to make the population more sustainable I've made another short list below with the minimal requirement of additional facilities like quarries, woodcutters, etc... (according to me)
=====================================================
Including optional buildings;
10 woodcutters required for charcoal upkeep (very rough estimate) * 49 tiles = 490 tiles required for woodcutters.
--------------------------------------------------------------------------------------------
I'd say it's possible to continuously sustain a still unhappy population of 5000 with 66 tiles left. These tiles could be spent on wells and hospitals to reduce the shrinking of the population.
The final conclusion is; you'd essentially have to throw out all happiness providing facilities like churches, libraries, and taverns to accomplish continuously sustaining 5000 pop.
Please keep in mind that these are all estimates and won't reflect on everyone's preferred play style.
Hopefully, this overly complicated "thought experiment" was of any use to anyone. Or maybe someone might enjoy reading through it.
Something to keep in mind is that you do get a Happiness boost if you can meet all the food needs of your Population (Wheat/Apples/Meat) and thus keep them in good Health.
I reached 7K happy and well fed people in easy mode.
The key is to have a very large land area with minimal water.
You can edit a map in creative mode, back out and play in easy or hard mode to get the map you want.