Days with dissolute man: Sir Francis (5)
I believe the answer is:
drake
'sir francis' is the definition.
(I've seen this in another clue)
'days with dissolute man' is the wordplay.
'days' becomes 'd' (abbreviation for days).
'with' means one lot of letters go next to another.
'dissolute man' becomes 'rake' (I've seen this in another clue).
'd'+'rake'='DRAKE'
(Other definitions for drake that I've seen before include "Male duck - circumnavigator" , "Nick" , "Male water-bird" , "Male bird" , "-'s Drum (Newbolt)" .)