No one wants a student around time of birth (5)
I believe the answer is:
natal
'of birth' is the definition.
(natal means relating to birth)
'no one wants a student around time' is the wordplay.
'no one' becomes 'na' (I can't explain this - if you can you should give a lot more credence to this answer).
'wants' says to put letters next to each other.
'student' becomes 'L' (as in L-plates for learner drivers).
'around' is an insertion indicator.
'time' becomes 't' (abbreviation).
'na'+'a'+'l'='naal'
'naal' placed around 't' is 'NATAL'.
Can you help me to learn more?
(Other definitions for natal that I've seen before include "Connected to birth" , "KwaZulu-____ , South African province" , "South African region" , "Of birth; former African republic" , "former SA province" .)