The most common and most likely answer to this crossword clue is the 5 letter word SHTUM
I've seen this crossword clue in The Times
S
H
T
U
M
More clues leading to the result SHTUM
Buddy explains!

The straight part
We know that "Dumb" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dumb = shtum.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 SHTUM mean?
SHTUM adjective- Silent; speechless; dumb.