Would stellar engines cause their planets to experience time dilation?

Question

For instance, if the stellar engine is moving the solar system at relativistic speeds, would, say, a 5,000 light year voyage be shorter for the inhabitants of a planet, or would the trip still take 5,000 years from their point of view, as they are not moving in their frame of reference, the star is.

Answer 1

From an external observer's point of view, the trip would take 5000 years, but for their point of view, the trip would take fewer years.

In their point of view, where "the destination is moving" at near the speed of light, length contraction means that they interpret the distance between them and the destination as being shorter. This is why they perceive a shorter time as well.