Turn out to demonstrate (5)
I believe the answer is:
prove
I believe this clue is a double definition.
'turn out' is the first definition.
('prove' can be a synonym of 'turn out')
'demonstrate' is the second definition.
('prove' can be a synonym of 'demonstrate')
'to' acts as a link.
(Other definitions for prove that I've seen before include "Verify" , "Demonstrate to be true" , "Show to be true" , "Establish the validity of" , "Demonstrate by evidence" .)