How common are three-character or five-character words/terms in Standard Mandarin? People often regard Chinese, including Standard Mandarin, as a monosyllabic language.

Classical Chinese apparently was a monosyllabic language, where words consisted of a single syllable (a single character also equals a single syllable).

Modern Standard Mandarin still has quite a few single-syllable words/terms, but more common are two-syllable (two-character) terms, to the point where many common words have an "empty" second syllable 子 literally meaning "child". This turns old single-syllable words into two syllable words, and it's a bit like a diminutive in western languages.

There are also very many 4-syllable words and terms. Some seem to be made up of two 2-syllable words and others seem to be made up of four single-syllable words.

But are there also three-syllable and five-syllable words? How common/rare are they?
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?