The most common and most likely answer to this crossword clue is the 5 letter word DORMS
D
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More clues leading to the result DORMS
Buddy explains!

The straight part
We know that "sleeping quarters" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sleeping quarters = dorms.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 DORMS mean?
DORMS noun- A room containing a number of beds (and often some other furniture and/or utilities) for sleeping, often applied to student and backpacker accommodation of this kind.
- A building or part of a building which houses students, soldiers, monks etc. who sleep there and use communal further facilities.
- A dormitory town.