It's a puzzle for an exhibitionist! (5)
I believe the answer is:
poser
I believe this is a double definition.
'it's a puzzle' is the first definition.
(poser can mean a mystery or puzzle)
'for an exhibitionist' is the second definition.
(poser is a kind of exhibitionist)
(Other definitions for poser that I've seen before include "Particularly baffling problem" , "Someone behaving so as to be noticed" , "One pretends to be something they are not" , "Show-off" , "difficult puzzle" .)