Very near the end (5)
I believe the answer is:
close
This might be a double definition.
'very near' is the first definition.
'close' can be an answer for 'near' (similar in meaning). I am unsure of the 'very' bit.
'the end' is the second definition.
(I've seen this before)
Can you help me to learn more?
(Other definitions for close that I've seen before include "Heavy" , "Shut - sultry" , "Near, mean or humid" , "residential street" , "Bar" .)