Went out, being old (5)
I believe the answer is:
dated
I believe this clue is a double definition.
'went out' is the first definition.
(dating is a kind of going out)
'old' is the second definition.
(dated can mean old or out of date)
'being' is the link.
(Other definitions for dated that I've seen before include "Went steady" , "Outmoded" , "Passe" , "Archaic; took out" , "Pass" .)