Elizabethan favourite died a dissolute man (5)
I believe the answer is:
drake
'elizabethan favourite' is the definition.
(I've seen this before)
'died a dissolute man' is the wordplay.
'died' becomes 'd' (abbreviation next to the year of someone's death).
'a dissolute man' becomes 'rake' (I've seen this before).
'd'+'rake'='DRAKE'
(Other definitions for drake that I've seen before include "Nick" , "English circumnavigator, d. 1596" , "world traveller" , "might be after a duck?" , "First English captain to sail round the world" .)