The most common and most likely answer to this crossword clue is the 5 letter word GREYS
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More clues leading to the result GREYS
Buddy explains!

The straight part
We know that "Regimental horses" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case regimental horses = greys.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 GREYS mean?
GREYS noun- An achromatic colour intermediate between black and white.
- An animal or thing of grey colour, such as a horse, badger, or salmon.
- An extraterrestrial humanoid with greyish skin, bulbous black eyes, and an enlarged head.
- To become grey.
- To cause to become grey.
- To turn progressively older, in the context of the population of a geographic region.
- To give a soft effect to (a photograph) by covering the negative while printing with a ground-glass plate.
- Grey trousers and/or jackets worn by prisoners on relatively formal occasions.