Thus, at about 0335 Greenwich Mean Time (GMT), the Moon will be only about 356,955 kilometers (221,802 miles) from Earth - its closest point (perigee) from Earth.
For your particular location on Earth, convert one of the (above) given times to your local times using one of the time conversion programs on the Web, such as TimeAndDate.com.
Of course, for those of you at locations in which the Moon will be at its closest point during the day, you will have to wait until night-time to see a brilliant Moon at almost its closest point to Earth.
In any case, during the nights of May 5 and May 6, 2012, we should be able to see quite a large sized Moon, assuming the sky is clear over your locality.
And, the Moon has not been this close to Earth in about 18 years, which makes this very close position to Earth especially interesting. It will allow skywatchers around the world a chance to see a really big Moon.
Some people call such a moon a SuperMoon, or even an Extreme SuperMoon. And, astronomers estimate that this Really Big Moon will be about 16% brighter than the average brightness of a Full Moon.