The most common and most likely answer to this crossword clue is the 5 letter word DOJOS
D
O
J
O
S
More clues leading to the result DOJOS
Buddy explains!

The straight part
We know that "fighting arenas" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fighting arenas = dojos.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 DOJOS mean?
DOJOS noun- The ring, made of compacted clay, in which a sumo wrestling match is held.
- A training facility, usually led by one or more sensei; a hall or room used for such training.
- (by extension) A room or other facility used for other activities, such as meditation or software development.