Finally, adult and a boy both playing part of first set (4,5)

'part of first set' is the definition.
(part of first set of teeth)

'finally adult and a boy both playing' is the wordplay.
'finally' indicates one should take the final letters.
'and' is a charade indicator (letters next to each other).
'playing' is an anagram indicator.
The final letter of 'adult' is 't'.
'a'+'boy'+'both'='aboyboth'
't' after 'aboyboth' is 'aboybotht'.
'aboybotht' is an anagram of 'BABY-TOOTH'.