Obsession with endless animal problem (5)
I believe the answer is:
mania
'obsession' is the definition.
(thesaurus)
'endless animal problem' is the wordplay.
'endless' means to remove the last letter.
'problem' indicates anagramming the letters.
'animal' with its last letter taken off is 'anima'.
'anima' anagrammed gives 'MANIA'.
'with' acts as a link.
(Other definitions for mania that I've seen before include "Frenzy" , "Craze; overexcitement" , "serious obsession" , "Violent madness or extreme enthusiasm" , "Excessive enthusiasm" .)