The most common and most likely answer to this crossword clue is the 2 plus 3 letter word OF AGE
O
F
A
G
E
More clues leading to the result OF AGE
- Half-hearted Mercian, say, rejected 18 as a rule
- Old enough finally to smoke a cigarette inside
- Love cigarette — ultimately smoke eighteen?
- Having acquired door key, maybe I’ll turn to check what’s following me
- Mature pain occupies heart of poem
- Mature student given work in Old English
- Grown-up having bother penetrating Old English
- Old enough to finally smoke drugs
Buddy explains!

The straight part
We know that "Grown-up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case grown-up = of age.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.