Our Moon reaches apogee, (greatest distance from Earth), on Wednesday October 25th. At that time the Moon will more or less be at a distance of 31.76 Earth diameters (404,154 km or 251,130 miles) from the Earth.
Does our Moon actually go around the Earth as this graphic shows? From our perspective on the Earth the Moon appears to circle around the Earth. However, in reality, the Moon orbits the Sun together with the Earth*
On the day of the apogee the 6-day old waxing crescent Moon will be over the southwestern horizon at sunset local time. Were it not so bright the glow of the Milky Way in the background might have been visible. Saturn is visible, but it is low above the horizon.
Read this very informative article about the Earth-Moon system and their orbital motions, written by Joe Hanson. “Do We Orbit the Moon?”