I'd quit Sunshine State for this girl (5)
I believe the answer is:
flora
'this girl' is the definition.
'i'd quit sunshine state' is the wordplay.
'quit' indicates named letters should be taken away.
'sunshine state' becomes 'florida' (synonyms).
'florida' with 'id' taken away is 'FLORA'.
'for' is the link.
(Other definitions for flora that I've seen before include "Lots of plants" , "Plant life of particular area" , "Plants of a region or age" , "Botanical specimens" , "Various plants" .)