Travel (how far?) into the future using a black hole and light-speed space craft?

A person is traveling in a space craft that was designed and built by sufficiently advanced aliens. This space craft left from Earth and is capable of traveling infinitely close to the speed of light. His/her journey takes him/her into space where the craft then orbits a black hole before sling shooting itself back to Earth. Is it feasible (through combined time distortion of both light speed travel and the proximity to the extreme gravity of the black hole) that when the traveler returns to Earth, millions of years have passed on Earth, despite the journey having only lasted no more than 10 years for the person inside the craft?

If so, depending on how close to the speed of light the space craft is traveling and the size of the black hole, how many millions of years is it reasonable to expect to have passed on Earth for a 10 year journey relative to the traveler? 5 million years? 50 Million? 500 Million? Less? More? etc.

For the sake of this question we can assume there is a black hole approximately 5 light years away from Earth.

EDIT: Thank you E Reid, Hyperion, user25972 and Justin Eiler for helping me realize my misunderstanding of the perceived time for our traveler and how a distance of 5 light years would be too short for him to experience 10 years of travel at near the speed of light.

posted about 8 years ago

jakecento‭

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