The most common and most likely answer to this crossword clue is the 5 letter word BLURT
I've seen this crossword clue in Independent
B
L
U
R
T
Buddy explains!

The straight part
We know that "Impulsively speak" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case impulsively speak = blurt.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 BLURT mean?
BLURT noun- An abrupt outburst.
- To utter suddenly and unadvisedly; to speak quickly or without thought; to divulge inconsiderately — commonly with out.