The feeling that an old barbarian went to church (5)
I believe the answer is:
hunch
'the feeling' is the definition.
(hunch is a kind of feeling)
'an old barbarian went to church' is the wordplay.
I cannot quite understand how this works, but
'barbarian' could be 'hun' (as in Atilla the Hun) and 'hun' is located in the answer.
'church' could be 'ch' (common abbreviation) and 'ch' is found within the answer.
This accounts for all the letters.
This explanation may well be incorrect...
'that' acts as a link.
Can you help me to learn more?
(Other definitions for hunch that I've seen before include "Premonition; hump" , "Intuition, suspicion" , "Bend over" , "Lump - intuitive feeling" , "Guess -- sit with bad posture" .)