Entertain American goddess (5)
I believe the answer is:
amuse
'entertain' is the definition.
(amuse can mean to entertain or divert)
'american goddess' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'goddess' becomes 'muse' (the muses in Greek myth).
'a'+'muse'='AMUSE'
(Other definitions for amuse that I've seen before include "Make (someone) laugh" , "interest" , "Beguile" , "Cause mirth - distract" , "Divert or entertain mildly" .)