The most common and most likely answer to this crossword clue is the 5 letter word SPRUE
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The straight part
We know that "asparagus" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case asparagus = sprue.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 SPRUE mean?
SPRUE noun- A tropical disease causing a sore throat and tongue, and disturbed digestion; psilosis.
- (founding) The hole through which melted metal is poured into the gate, and thence into the mold.
- (founding) Material that cools in the feed channels to a mold.
- To remove the sprues (material left in feed channels) from a cast piece.