Six storey pre fabricated flats in 500BC with piped water & sewerage Carthage, Engineering an Empire

The Carthaginian buildings were six-stories high according to Appian:

Now Scipio hastened to the attack of Byrsa, the strongest part of the city, where the greater part of the inhabitants had taken refuge. There were three streets ascending from the forum to this fortress, along which, on either side, were houses built closely together and six stories high, from which the Romans were assailed with missiles. They were compelled, therefore, to possess themselves of the first ones and use those as a means of expelling the occupants of the next.

When they had mastered the first, they threw timbers from one to another over the narrow passageways, and crossed as on bridges. While war was raging in this way on the roofs, another fight was going on among those who met each other in the streets below. All places were filled with groans, shrieks, shouts, and every kind of agony. Some were stabbed, others were hurled alive from the roofs to the pavement, some of them alighting on the heads of spears or other pointed weapons, or swords. No one dared to set fire to the houses on account of those who were still on the roofs, until Scipio reached Byrsa. Then he set fire to the three streets all together, and gave orders to keep the passageways clear of burning material so that the army might move back and forth freely.
(Punic Wars, 128)

Excavations have revealed large apartment buildings with strong walls which Hoyos believes could have supported six-stories (Hoyos, The Carthaginians, p.85)