Crew of Apollo 13. They went a little further beyond the moon than the other Apollo crews since they just whipped around it to come back home and didn't slow down to orbit it. About 245,000 miles.
At its closest point, known as the perihelion, the Moon is only 363,104 km (225,622 miles). And at its most distant point, called aphelion, the Moon gets to a distance of 406,696 km (252,088 miles).
Apollo 13 Crew
NASA - Apollo 13