Survives very boring falsehoods (5)
I believe the answer is:
lives
'survives' is the definition.
('live' can be a synonym of 'survive')
'very boring falsehoods' is the wordplay.
'very' becomes 'v' (common abbreviation).
'boring' indicates putting letters inside (to bore something can mean to drill into it).
'falsehoods' becomes 'lies' (lie is a kind of falsehood).
'v' put inside 'lies' is 'LIVES'.
(Other definitions for lives that I've seen before include "Resides" , "Exists" , "Elvis (anag) - is not dead" , "See 5" , "Biographies" .)