The most common and most likely answer to this crossword clue is the 7 plus 8 letter word PERFECT INTERVAL
I've seen this crossword clue in The Times
P
E
R
F
E
C
T
I
N
T
E
R
V
A
L
Buddy explains!
The straight part
We know that "Fourth or fifth, maybe" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fourth or fifth, maybe = perfect interval.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.