The most common and most likely answer to this crossword clue is the 9 plus 5 letter word ANYBODY'S GUESS
I've seen this crossword clue in The Times
A
N
Y
B
O
D
Y
'
S
G
U
E
S
S
Buddy explains!
The straight part
We know that "unsolvable" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unsolvable = anybody's guess.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.