The most common and most likely answer to this crossword clue is the 1 plus 3 plus 5 letter word A BAD LOSER
I've seen this crossword clue in Financial Times
A
B
A
D
L
O
S
E
R
Buddy explains!
The straight part
We know that "Crybaby" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case crybaby = a bad loser.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.