I went back to my country on May fourth.
Golden week is in May.
I’m going to a river in May.
The moon kanji also represents a month, so when you have five of these months, what month of the year is it? That would be May, the greatest month of the year (because it has towel day in it!).
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well. Also, this is a specific month, so it uses the がつ reading.