Floor 0507, or more simply 507, was one of over a thousand decks on a Mondasian colony ship. The floor contained the largest of the ship's solar farms.
When the colony ship almost traversed into a black hole, each of the ship's floors was affected by time dilation. Located approximate to the middle of the ship, time travelled faster on floor 507 than on the floors above, but slower than on the floors below. (TV: World Enough and Time) The floor appeared to be perfectly habitable, the residents here being blissfully unaware they lived on a spaceship. The time dilation with the other floors was still years in difference; the Cybermen down below had enough time reach their maximum upgrade over the two weeks the Doctor and his companions were there. (TV: The Doctor Falls)
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Many years before Bill Potts arrived on floor 1056, there was an expedition from 1056 to 507. The Mondasians who went on the expedition never returned. (TV: World Enough and Time) It was revealed this group had actually been subdued by the residents of floor 507, being shot down by night and strung up on crucifixes by day. (TV: The Doctor Falls).