Happening around the fifth, something burning this month (8)
I believe the answer is:
november
'month' is the definition.
(November is a month)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for november that I've seen before include "Several days" , "Eleventh month" , "Taunt, food in trap" , "N in radio comms" , "bit of a fall" .)