The most common and most likely answer to this crossword clue is the 5 letter word DELAY
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Buddy explains!

The straight part
We know that "put off" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case put off = delay.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 DELAY mean?
DELAY noun- A period of time before an event occurs; the act of delaying; procrastination; lingering inactivity.
- An audio effects unit that introduces a controlled delay.
- To put off until a later time; to defer.
- To retard; to stop, detain, or hinder, for a time.
- To allay; to temper.
- To dilute, temper.
- To assuage, quench, allay.