Old lady captivates a doctor with snake (5)
I believe the answer is:
mamba
'snake' is the definition.
(mamba is a kind of snake)
'old lady captivates a doctor' is the wordplay.
'old lady' becomes 'ma'.
'captivates' indicates putting letters inside.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'a'+'mb'='amb'
'ma' going around 'amb' is 'MAMBA'.
'with' is the link.
(Other definitions for mamba that I've seen before include "one venomous" , "Large African snake" , "Poisonous creature" , "It may be deadly" , "serpent" .)