Our Moon reaches apogee, (greatest distance from Earth), for this orbit, on Monday 18th. At that time the 26.5-day old waning crescent Moon will be at a distance of 31.88 Earth diameters 252,028 miles (405,600 km) from the Earth.
On the day of the apogee the thin waning crescent Moon rises about 1-2 hours before sunrise local time. Looking carefully with binoculars you may be able to see nearby 4th magnitude star 20 Ceti, one of the many stars that are part of the constellation Cetus the Whale.
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*