Desire to hurt or offend (5)
I believe the answer is:
spite
I believe this is a double definition.
'desire to hurt' is the first definition.
(I've seen this before)
'offend' is the second definition.
(I know that offend can be written as spite)
(Other definitions for spite that I've seen before include "animosity" , "Rancour" , "Desire to hurt or annoy" , "Bitchiness or malice" , "Hatred" .)