The most common and most likely answer to this crossword clue is the 3 plus 2 plus 5 letter word END OF STORY
I've seen this crossword clue in The Times
E
N
D
O
F
S
T
O
R
Y
Buddy explains!
The straight part
We know that "that’s that!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s that! = end of story.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.