Assume a college student from 2018 accidentally traveled to 2023. He is accidentally taken by an alien spaceship that travels close to the speed of light away from earth and then travels back. He is put back to the place where he was taken.
The question is how can he prove to the people in 2023 that he has time traveled, against other possibilities, such as running away from school.
First, necessary step - establish identity
He's identical to his document pictures from five years before, so that plus DNA matching with family members can establish he's who he's saying he is. So, we know that he should be around 25 years old.
Now how to prove he's actually 20?
Standard radioisotope dating (e.g. 14C) would not work. Radioisotope dating only measures time since loss of equilibrium, which usually happens at death. But even if the guy had died on the ship, that time would be his local elapsed time, so just a few minutes; there would be no clue as to how long he had lived before meeting his end.
If something had happened outside in those five years, and the guy did not show the signs, then yes, it would work - but the premise is that nothing of the kind happened.
- update: it might work, because something did happen outside in that time. There are environmental isotopes that decay naturally and, of course, most living beings are at equilibrium with them. But our guy isn't - he's got in his body five years of undecayed radioisotopes. This could be another factor to take into account, even if it would be probably explained away as natural variation or contamination by those same isotopes.
Chances are that his clothes and appearance were recorded in selfies, videos and memories from five years back. He's still almost identical. While possible, this is really unlikely - a 25-years old is quite different from a 20-years old.
It is possible to question him on everything that went on in the weeks before his disappearance, five years ago for the interrogators, a few weeks for him. Were he an impostor, he might have studied again whatever examinations he gave last, and might have painstakingly reconstructed all the facts from those days and learned them by heart. He wouldn't be able to fool police detectives, whose job it is to see through alibis. If he were simulating, he would remember too little, or too much, in ways that are obvious to an expert. So either he's telling the truth or he's been coached by an expert on how to lie.
Growth in the interval 15..25 years can be analyzed quite effectively and will say that the guy is now 20 years old, give or take three years. The possibility he's actually 25 is still open, but not very likely.
After he disappeared, almost surely some kind of DNA sampling of the area was done; and it's very likely that some DNA samples from five years back can be recovered anyway.
That, plus PCR amplification, would show that either he's being time-shifted five years in the future, or something did a really weird number on his telomeres.
Probably nobody would believe in a starship, and people would rather assume some strange time-warp effect - the time equivalent of Tay al-Arz - or some "Bermuda Triangle" time-stasis, or ultra-black government experiments. I bet lots of people would start combing the disappearance area looking for clues, measuring radioactivity, magnetic fields, and wearing tinfoil hats and dowsing rods...
But the fact that he somehow skipped five years of his life would be quite hard to deny.