Greeting school quintet (4-4)

I believe the answer is:

high-five

'greeting' is the definition.
(I've seen this before)

'school quintet' is the wordplay.
'school' becomes 'high' (high school is a kind of school).
'quintet' becomes 'five' ('five' can be a synonym of 'quintet').
'high'+'five'='HIGH-FIVE'

I've seen this clue in The Times.

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