Religious books are about Greek goddess (5)
I believe the answer is:
erato
'greek goddess' is the definition.
(one of the Greek muses)
'religious books are about' is the wordplay.
'religious books' becomes 'ot' (Old Testament).
'about' says the letters should be written backwards.
'ot'+'are'='otare'
'otare' backwards is 'ERATO'.
(Other definitions for erato that I've seen before include "Source of poetic inspiration" , "One of the Muses" , "Poet's inspiration" , "Arts patron" , "daughter of Zeus" .)