Copes badly, to an extent (5)
I believe the answer is:
scope
'to an extent' is the definition.
(scope is a kind of extent)
'copes badly' is the wordplay.
'badly' indicates an anagram.
'copes' is an anagram of 'SCOPE'.
(Other definitions for scope that I've seen before include "Capacity" , "Extent; viewer (colloq.)" , "Space for movement or activity" , "Range of action" , "Ambit, compass" .)