The most common and most likely answer to this crossword clue is the 5 letter word DEMOS
I've seen this crossword clue in The Times
D
E
M
O
S
Buddy explains!

The straight part
We know that "masses" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case masses = demos.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 DEMOS mean?
DEMOS noun- A demonstration or visual explanation.
- A recording of a song meant to demonstrate its overall sound for the purpose of getting it published or recorded more fully.
- An example of a product used for demonstration and then sold at a discount.
- A march or gathering to make a political protest.
- An edition of limited functionality to give the user an example of how the program works.
- A non-interactive audiovisual computer program developed by enthusiasts to demonstrate the capabilities of the machine. See demoscene.
- A democrat.
- (collective) A demographic group.
- Demolition.