Can anyone explain these lights I saw in the sky in May?

You've provided quite a bit of good information, such as your location and the date and time. Some important details are lacking, such as the direction and altitude of the lights. You've estimated the altitude based on umptions about distance, which is impossible to know in the dark with an unknown object. A scientist would prefer an angular distance, an altitude estimated in degrees between the horizon (0�) and the zenith overhead (90�). My guess is that you were seeing a formation of stars or a cluster of satellites, such as an NOSS triplet.