The most common and most likely answer to this crossword clue is the 5 letter word CAVIL
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The straight part
We know that "make petty complaints" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make petty complaints = cavil.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 CAVIL mean?
CAVIL noun- A petty or trivial objection or criticism.
- To criticise for petty or frivolous reasons.