Relish got distributed around America (5)
I believe the answer is:
gusto
'relish' is the definition.
('gusto' can be a synonym of 'relish')
'got distributed around america' is the wordplay.
'distributed' indicates an anagram.
'around' means one lot of letters goes inside another.
'america' becomes 'us' (abbreviation for the United States).
'got' is an anagram of 'gto'.
'gto' enclosing 'us' is 'GUSTO'.
(Other definitions for gusto that I've seen before include "Zest, zeal" , "Great enjoyment, vigour" , "Spirit" , "Great enjoyment in doing something" , "Hearty enjoyment" .)