The most common and most likely answer to this crossword clue is the 5 letter word FILTH
I've seen this crossword clue in The Daily Telegraph
F
I
L
T
H
More clues leading to the result FILTH
Buddy explains!

The straight part
We know that "Disgusting dirt" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case disgusting dirt = filth.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 FILTH mean?
FILTH noun- Dirt; foul matter; that which soils or defiles.
- Smut; that which sullies or defiles the moral character; corruption; pollution.
- (with definite article) The police.
- A vile or disgusting person.
- Weeds growing on pasture land.