The most common and most likely answer to this crossword clue is the 5 letter word LOFTS
I've seen this crossword clue in The Daily Telegraph
L
O
F
T
S
Buddy explains!
The straight part
We know that "Pigeon sheds" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pigeon sheds = lofts.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 LOFTS mean?
LOFTS noun- (except in derivatives) air, the air; the sky, the heavens.
- An attic or similar space (often used for storage) in the roof of a house or other building.
- The thickness of a soft object when not under pressure.
- A gallery or raised apartment in a church, hall, etc.
- The pitch or slope of the face of a golf club (tending to drive the ball upward).
- A floor or room placed above another.
- To propel high into the air.
- To fly or travel through the air, as though propelled
- To throw the ball erroneously through the air instead of releasing it on the lane's surface.
- To furnish with a loft space.