Animal with a sore throat, by the sound of it (5)
I believe the answer is:
horse
'animal' is the definition.
(I know that horse is a type of Equidae)
'with a sore throat by the sound of it' is the wordplay.
'with a sore throat' becomes 'hoarse' (hoarse means having a sore throat).
'by the sound of it' shows a homophone (sound like).
'hoarse' is a homophone of 'HORSE'.
(Other definitions for horse that I've seen before include "Arab" , "Suffolk punch" , "punch, perhaps" , "Eg, mare" , "Cavalry - gymnastic apparatus" .)