The most common and most likely answer to this crossword clue is the 5 letter word APACE
I've seen this crossword clue in The Times
A
P
A
C
E
More clues leading to the result APACE
- Quickly take horse from native American
- Native American wanting horse with speed
- Member of American tribe gets horse going quickly
- Top pilot crosses Patagonia's borders quickly
- Fast one taking secretary in
- Hard top car’s taken off at speed
- Native American leaving hospital fast
- Dad turned expert at a rate of knots
- Military helicopter leaves hospital very quickly
- Top grade carbon copy’s acquired quickly
Buddy explains!

The straight part
We know that "with speed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case with speed = apace.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 APACE mean?
APACE adverb- Quickly, rapidly, with speed.