State of humanity, I admitted, close to collapse (5)
I believe the answer is:
maine
'state' is the definition.
(US state)
'humanity i admitted close to collapse' is the wordplay.
'humanity' becomes 'man' (synonyms).
'admitted' means one lot of letters goes inside another (inserted letters are let in or admitted).
'close to' suggests the final letters (the close of something is the end).
The final letter of 'collapse' is 'e'.
'man' going around 'i' is 'main'.
'main'+'e'='MAINE'
'of' is the link.
(Other definitions for maine that I've seen before include "New England state" , "North-easterly US state" , "The USA's Pine Tree State" , "somewhere in America" , "N. US Atlantic state" .)