Passing infatuation is extremely close (4,2,5)
I believe the answer is:
hand in glove
'extremely close' is the definition.
(I've seen this before)
'passing infatuation' is the wordplay.
'passing' becomes 'handing' ('hand' can be a synonym of 'pass').
'infatuation' becomes 'love' (I can't justify this - if you can you should believe this answer much more).
'handing'+'love'='HAND-IN-GLOVE'
'is' is the link.
Can you help me to learn more?
(Other definitions for hand in glove that I've seen before include "Give up boxing" , "very much a description of close relationship?" , "Working together" , "On intimate terms" , "Offering affection" .)