The most common and most likely answer to this crossword clue is the 5 letter word MOIST
I've seen this crossword clue in The Times
M
O
I
S
T
More clues leading to the result MOIST
- Somewhat wet politicians at centre in majority
- Damp fog — nothing visible in that
- Man pulling back stone getting sweaty?
- Left-winger, but not a wet
- Nearly all admitting India's humid
- Supporter of Chinese communist, not a little wet
- Tearful second, and the one ahead
- Como is too wet in the middle!
- Film bagging Oscar is not dry
- Damp from fine spray carrying over
Buddy explains!

The straight part
We know that "Damp" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case damp = moist.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MOIST mean?
MOIST verb- To moisten.
- Slightly wet; characterised by the presence of moisture, not dry; damp.
- Of eyes: tearful, wet with tears.
- Of weather, climate etc.: rainy, damp.
- Pertaining to one of the four essential qualities formerly believed to be present in all things, characterised by wetness.
- Watery, liquid, fluid.
- Characterised by the presence of pus, mucus etc.
- Sexually lubricated (of the vagina); sexually aroused, turned on (of a woman).