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

The straight part
We know that "very long time cycle" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very long time cycle = saros.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 SAROS mean?
SAROS noun- (history, Babylon) A quantity of 3600, such as a period of 3600 years.
- A period of 223 synodic months (approximately 18 years 11 days 8 hours), after which the relative positions of the earth, sun and moon recur, used to predict eclipses.