The most common and most likely answer to this crossword clue is the 5 letter word  PHEW
I've seen this crossword clue in The Guardian
Â
P
H
E
W
Buddy explains!

The straight part
We know that "what a relief!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what a relief! = Â phew.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  PHEW mean?
 PHEW interjection- Used to express relief of tension, fatigue, or surprise.
- Used to show disgust.