"Imagine a 15 year-old traveling at 99.5 percent the speed of light for 5 years (from the astronauts perspective). When the 15 year-old gets back to earth, according to NASA, he would be only 20 years old. His classmates, however, would be 65 years old".

Problem 1: To an observer on earth, the astronaut is in motion. To the astronaut, the earth is in motion. That implies that both the observer and the astronaut would be aging more rapidly in the other person's system. That would make the astronaut the same age as his classmates.

Problem 2: If the astronaut is traveling for 5 years and ends up on earth, this implies a round trip. On a round trip the effects encountered going away should be cancelled by the effects encountered on the return trip. That would make the astronaut the same age as his classmates.

Where has my thinking gone wrong?