A journal whose days are numbered (5)
I believe the answer is:
diary
'a journal' is the definition.
('diary' can be a synonym of 'journal')
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for diary that I've seen before include "personal account" , "Record of events" , "Pepys' daily record" , "Personal journal" , "Personal record book" .)