I came in very damp (5)
I believe the answer is:
moist
'very damp' is the definition.
'moist' can be an answer for 'damp' (synonyms). I'm unsure of the 'very' bit.
'i came in' is the wordplay.
'came' becomes 'most' (I can't explain this - if you can you should give a lot more credence to this answer).
'in' is an insertion indicator.
'i' inserted inside 'most' is 'MOIST'.
Can you help me to learn more?
(Other definitions for moist that I've seen before include "Damp or clammy" , "sloppy" , "Affected by tears, perhaps" , "Slightly wet, damp" , "bit wet" .)