Beginning to shake cough in humble dwelling (5)
I believe the answer is:
shack
'humble dwelling' is the definition.
(I've seen this in another clue)
'beginning to shake cough' is the wordplay.
'beginning to' says to take the initial letters.
'cough' becomes 'hack' (hacking is a kind of coughing).
The initial letter of 'shake' is 's'.
's'+'hack'='SHACK'
'in' acts as a link.
(Other definitions for shack that I've seen before include "Roughly built hut" , "Rough hut or cabin" , "building made of wood?" , "Crudely built hut" , "Crude dwelling" .)