The most common and most likely answer to this crossword clue is the 5 letter word PETIT
P
E
T
I
T
Buddy explains!

The straight part
We know that "Insignificant" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case insignificant = petit.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 PETIT mean?
PETIT noun- (usually in the plural) A little schoolboy.
- A kind of pigeon.
- (of size) Petite: small, little.
- Petty, in its various senses:
- The size of type between minion and bourgeois, standardized as 8-point.