The most common and most likely answer to this crossword clue is the 5 letter word DRAT!
I've seen this crossword clue in The Guardian
D
R
A
T
!
Buddy explains!
The straight part
We know that "that makes me angry" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that makes me angry = drat!.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 DRAT! mean?
DRAT! verb- To damn or curse.
- Expressing anger, annoyance or frustration.