1. I grew 5 cm since last year!

2. I grew by 5 cm since last year!

(In #1, was 'by' omitted before '5 cm'? Then, 'grew' was used as an intransitive verb. If not, 'grew' was used as a transitive verb and '5 cm' is the object of 'grew.' Would you let me know about that?)

You're right. The verb grow can be either transitive or intransitive.

Although # 1 is most common, # 2 is also correct.

Thank you. Then, do you mean in #1, 'grew' was used as a transitive verb and 5 cm is the object of 'grew'?

Right.

In the sentence "I grew 5 cm since last year," the word "by" is indeed omitted before "5 cm." This usage is common when discussing changes in height or length. In this context, "grew" is used as an intransitive verb, meaning it doesn't require an object. The phrase "5 cm" functions as an adverbial phrase, indicating the extent or manner of growth. So, without the word "by," there is no direct object in the sentence.