Good, but a 4 levels house, with the numerous families typical of pre-modern societies, would easily host 50 or more people imho. 5000 buildings, more like 100k people at least.
Look also at this estimates of population density for ancient cities: https://faculty.washington.edu/modelski/WCITI2.html
~500 people per hct seems pretty normal, mean estimate is 350people/hct, that seems a lot denser that you imply for your 4x3 Km map.