The most common and most likely answer to this crossword clue is the 2 plus 2 plus 3 letter word OF AN AGE
I've seen this crossword clue in Financial Times
O
F
A
N
A
G
E
Buddy explains!
The straight part
We know that "Having so many years/belonging to a particular generation" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case having so many years/belonging to a particular generation = of an 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.