To make a statement that's extreme (5)
I believe the answer is:
pique
'to make' is the definition.
(I know that pique is a more specific form of the action anger)
'a statement that's extreme' is the wordplay.
'a statement' shows a homophone (sound like) (how it might sound when said or stated).
'that's extreme' becomes 'peak' (peak is a kind of extreme).
'peak' sounds like 'PIQUE'.
(Other definitions for pique that I've seen before include "Bad temper" , "Hurt feelings" , "Dudgeon" , "A feeling of hurt pride" , "Stimulate (one's curiosity)" .)