Same problem, having registered horses (5)

I believe the answer is:

mares

'horses' is the definition.
(female horses)

'same problem having registered' is the wordplay.
'problem' indicates anagramming the letters.
'having' is an insertion indicator.
'registered' becomes 'R' (abbreviation, as in registered trademark).
'same' anagrammed gives 'maes'.
'maes' going around 'r' is 'MARES'.

(Another definition for mares that I've seen is " Female horses".)

I've seen this clue in The Mirror.

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