The 1st quarter moon comes on May 12 at 1:12 UTC. At European and American time zones, you’ll find it high up at sunset on May 10 and 11. It appears nearly or completely half-illuminated, like half a pie.
You can’t see a new moon; it’s between the Earth and sun and crosses the sky with the sun throughout the day. Will you see the returning young crescent moon in the west after sunset May 5? Maybe, with effort. The young moon will sweep past Mars around May 6 to 8.