Perhaps mount height, or both sides of slope (5)
I believe the answer is:
horse
'perhaps mount' is the definition.
(I know that mount is a type of horse)
'height or both sides of slope' is the wordplay.
'height' becomes 'h' (abbreviation in geometry).
'both sides of' says to hollow out the word (remove centre letters) (only the letters on the sides remain).
'slope' with its middle removed is 'se'.
'h'+'or'+'se'='HORSE'
(Other definitions for horse that I've seen before include "Equine animal" , "Animal featuring in the sport of kings" , "Mount" , "Might one be up on this" , "Vaulting --; -- sense" .)