Burrow, rummage (5)
I believe the answer is:
delve
I believe this is a double definition.
'burrow' is the first definition.
(I know that burrow is a more specific form of the action delve)
'rummage' is the second definition.
(I've seen this before)
(Other definitions for delve that I've seen before include "Look closely (into)" , "Hollow" , "Make painstaking enquiries (into something)" , "Dig - investigate" , "Intensively research (into something)" .)