According to our current understanding of physics, it is not possible for any object, including a ship, to travel faster than the speed of light. The theory of relativity, specifically special relativity, prohibits objects with mass from reaching or exceeding the speed of light.
As an object with mass approaches the speed of light, its energy requirements become infinite. It would need an infinite amount of energy to accelerate it to that speed, which is not feasible. Additionally, as an object with mass accelerates, its mass increases, making it even more difficult to reach the speed of light.
Regarding black holes, they are incredibly dense objects with a gravitational pull so strong that not even light can escape from their vicinity. Once an object, including a ship, crosses the event horizon of a black hole (the point of no return), it is inevitably drawn into the black hole's singularity, where our current understanding of physics breaks down.
Inside the black hole, the gravitational forces become extremely intense, leading to a phenomenon known as spaghettification. In this process, the tidal forces of the black hole stretch the object into long, thin shapes resembling spaghetti. It is not possible for any matter, including a ship, to survive this process intact.
Therefore, the concept of a ship traveling through a black hole at faster-than-light speeds is not consistent with our current scientific understanding.