The most common and most likely answer to this crossword clue is the 5 letter word PESTS
I've seen this crossword clue in The Daily Telegraph
P
E
S
T
S
More clues leading to the result PESTS
Buddy explains!

The straight part
We know that "Nuisances" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nuisances = pests.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 PESTS mean?
PESTS noun- A plague, pestilence, epidemic
- Any destructive insect or caterpillar that attacks crops or livestock; an agricultural pest.
- An annoying person, a nuisance.
- An animal regarded as a nuisance, destructive, or a parasite, vermin.
- An invasive weed.