Serious — offensive (5)
I believe the answer is:
nasty
This clue is a double definition.
'serious' is the first definition.
(thesaurus)
'offensive' is the second definition.
(I've seen this before)
(Other definitions for nasty that I've seen before include "Disgusting" , "Obscene" , "Beastly" , "rank" , "Not nice" .)