Dead wrong about the tango being old-fashioned (5)
I believe the answer is:
dated
'old-fashioned' is the definition.
(dated can mean old-fashioned)
'dead wrong about the tango' is the wordplay.
'wrong' is an anagram indicator.
'about' indicates putting letters inside.
'the tango' becomes 'T' (phonetic alphabet: alpha, bravo, charlie etc.).
'dead' with letters rearranged gives 'daed'.
'daed' placed around 't' is 'DATED'.
'being' is the link.
(Other definitions for dated that I've seen before include "Revealed the age of" , "Walked out with" , "Old fashioned" , "Old-fashioned" , "No longer fashionable or current" .)