Show-off has problem (5)
I believe the answer is:
poser
I believe this is a double definition.
'show-off' is the first definition.
(poser is a kind of show-off)
'problem' is the second definition.
(poser is a kind of problem)
'has' is the link.
(Other definitions for poser that I've seen before include "Show-off" , "question master?" , "Tricky problem" , "Puzzle using ropes" , "Problem set by the model" .)