To this question, a person who believes in the theory of the lunar conspiracy will answer that a person has not been further than the orbit of the Earth, and a person who shares the opinion of all any serious experts in the space industry will say that the maximum distance from the Earth was achieved during one of the American landings on the Moon. Both of them will be wrong.
The farthest from Earth were the astronauts of the Apollo 13 spacecraft, and this happened «thanks to» a series of accidents on board that almost caused the death of the entire crew.
On April 11, 1970, the Apollo 13 spacecraft with astronauts James Lovell, John Swygert, Fred Hayes flew to the Moon. This was supposed to be the third (after Apollo 11 and Apollo 12) landing of the Americans on a natural satellite of the Earth. However, things went wrong. Due to inconsistency in the actions of several private contractors in the design and manufacture of ship parts, an accident occurred on board on the third day of the flight. Of course, there could be no question of any landing on the moon after this — it was necessary to save the crew.
Despite the fact that the accident was only the first, in a whole series of accidents and malfunctions, thanks to both incredible luck and professionalism, composure and courage of the astronauts, the ship was returned to Earth safely. However, during the maneuvers, the Apollo 13 spacecraft circled the Moon, and it was at the moment of this flyby that the astronauts were farther from the Earth than anyone else before or after them. This distance was 401,056 kilometers.
This happened because during this flight the Moon was close to the apogee of its orbit, i.e. to the point of greatest distance from the Earth. All other flights, including manned flyby of the Moon and all 6 landings, were carried out at a time when the Moon was significantly closer to the Earth, for example, the landing of Neil Armstrong and Edwin Aldrin was carried out at a distance between the Earth and the Moon of about 370,500 kilometers.
Thus, astronauts James Lovell, John Swigert and Fred Hayes have gone down in history twice. First, as people who have traveled further from the Earth than anyone else. And secondly, with the phrase «Houston, we have a problem.» Yes, yes they are.
P.S. In general, the phrase sounded «Houston, we just had a problem», but does it matter?