How common are three-character or five-character words/terms in Standard Mandarin?
I don't have any specific frequency data for you, but three and five syllable words certainly do exist.  Three syllable words are certainly less common than two syllable words but they do compose a decent amount of anyone's basic vocabulary (consider 毕业生), and five syllable words are fairly rare and restricted to certain proper nouns and the occasional fixed expression.

Of course, as words get longer, it is less and less clear what counts as a single word.  ABC has 应届毕业生 as one word, but is it really one word or is it a stock expression composed of two words?