The most common and most likely answer to this crossword clue is the 5 letter word STINK
I've seen this crossword clue in The Guardian
S
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Buddy explains!

The straight part
We know that "Nasty smell" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nasty smell = stink.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 STINK mean?
STINK noun- A strong bad smell.
- A complaint or objection.
- To have a strong bad smell.
- To be greatly inferior; to perform badly.
- To give an impression of dishonesty or untruth.
- To cause to stink; to affect by a stink.
- Bad; inferior; worthless.
- Bad-smelling, stinky.