Went out, being no longer fashionable (5)
I believe the answer is:
dated
This clue is a double definition.
'went out' is the first definition.
(dating is a kind of going out)
'no longer fashionable' is the second definition.
(dated means old-fashioned)
'being' is the link.
(Other definitions for dated that I've seen before include "Old fashioned" , "not without romantic engagements" , "Outmoded" , "Obsolete" , "Revealed the age of" .)