Investigate why it's a bit of a problem to live (5)
I believe the answer is:
probe
'investigate why' is the definition.
'probe' can be an answer for 'investigate' (probing is a kind of investigating). I'm unsure of the 'why' bit.
'a bit of a problem to live' is the wordplay.
'a bit of' indicates taking the first letters.
'to live' becomes 'robe' (I am not sure about this - if you are sure you should believe this answer much more).
The initial letter of 'problem' is 'p'.
'p'+'robe'='PROBE'
'it's' is the link.
Can you help me to learn more?
(Other definitions for probe that I've seen before include "Question or examine closely" , "Spacecraft; investigation" , "Inquiry" , "Question or examine thoroughly" , "Poke into" .)