Danes out of hilly area (5)
I believe the answer is:
andes
'hilly area' is the definition.
Although both the answer and definition are singular nouns, I cannot see how they can define each other.
'danes out' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'danes' is an anagram of 'ANDES'.
'of' acts as a link.
Can you help me to learn more?
(Other definitions for andes that I've seen before include "Mountains in west" , "Peak District" , "danes found in mountains" , "A geographical feature" , "The range of llamas?" .)