five-hitter vs baseball game

five-hitter and baseball game both are nouns.

Word	Noun	Adjective	Verb	Adverb
five-hitter	Yes	No	No	No
baseball game	Yes	No	No	No

As nouns, baseball game is a hypernym of five-hitter; that is, baseball game is a word with a broader meaning than five-hitter:

five-hitter: a game in which a pitcher allows the opposing team 5 hits
baseball game: a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs

Other hypernyms of five-hitter include ball, baseball.

five-hitter (noun)	baseball game (noun)
a game in which a pitcher allows the opposing team 5 hits	a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs