Becoming extinct due to extremely deadly inborn disease (5,3)
I believe the answer is:
dying out
'becoming extinct' is the definition.
(I've seen this before)
'extremely deadly inborn disease' is the wordplay.
I cannot really see how this works, but
'disease' could be 'gout' (gout is a kind of health problem) and 'gout' is found in the answer.
This explanation may well be incorrect...
'due to' is the link.
Can you help me to learn more?
(Other definitions for dying out that I've seen before include "Disappearing" , "Becoming extinct" .)