The most common and most likely answer to this crossword clue is the 5 letter word PEEVE
I've seen this crossword clue in Independent
P
E
E
V
E
More clues leading to the result PEEVE
- Get annoyed with record turning up the day before
- Annoy class in gym the day before
- Bug in water very close to surface
- Water vole eviscerated bug
- Grievance leads to volcanic eruption by Jimmy
- Annoy first lady recording towards the back
- Vexation shown by extremely perverse girl
- Hope everyone can contain bug
- Get on someone’s nerves, training the night before
- Cause irritation using drill on previous day
Buddy explains!

The straight part
We know that "Vexation" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vexation = peeve.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 PEEVE mean?
PEEVE noun- An annoyance or grievance.
- To annoy; vex.