Hollywood success means nothing to Mark (5)
I believe the answer is:
oscar
'hollywood success' is the definition.
(film award won in Hollywood)
'nothing to mark' is the wordplay.
'nothing' becomes 'o' (O resembles 0).
'to mark' becomes 'scar' (mark left by an injury).
'o'+'scar'='OSCAR'
'means' acts as a link.
(Other definitions for oscar that I've seen before include "The familiar Mr Wilde, playwright" , "Librettist Hammerstein, d. 1960" , "One close to Mike" , "Man" , "Phonetic code for O" .)