Firework do Anne and Carl organised around the fifth of November (5,6)
I believe the answer is:
roman candle
'firework' is the definition.
(Roman candle is an example)
'do anne and carl organised around the fifth of november' is the wordplay.
'and' means one lot of letters go next to another.
'organised' is an anagram indicator.
'around' means one lot of letters goes inside another.
'the fifth of november' becomes 'm' (fifth letter of the word 'November').
'anne' put after 'carl' is 'carlanne'.
'do'+'carlanne'='docarlanne'
'docarlanne' is an anagram of 'roancandle'.
'roancandle' going around 'm' is 'ROMAN CANDLE'.
(Other definitions for roman candle that I've seen before include "Pyrotechnic device" , "Example of fireworks" , "Firework projecting succession of coloured stars" , "Cylindrical firework" , "A cold manner (anag) -- firework" .)