Kimchibokkeumbap is correct, the sentence as written is ambiguous and you do not, with certainty, know which award was won. However, I believe the writer intended the sentence to imply that Brad Pitt has won a Golden Globe Award (which he has). It would have been better if the writer had reversed the clauses:
Pitt has received five Golden Globe Award nominations, winning one, and two Academy Award
This makes it clear that "won" refers to the Golden Globe Award nominations.