England set Australia a world record 546 on Saturday to win the fifth and final Ashes Test after Jonathan Trott (119) scored a century on his Test debut.
At the close of the third day, Australia had scored 80 for no wicket with six sessions remaining.
They need at least a draw to retain the Ashes after squaring the series 1-1 in the fourth Test at Headingley.
West Indies recorded the highest fourth innings winning total six years ago when they reached 418 for seven against Australia at St John's in Antigua.
Trott, who was run out for 41 in the first innings, became the first England player since Graham Thorpe in 1993 to score an Ashes century on debut.
Andrew Strauss and Trott took the overnight total of 58 for three to 157 before the England captain was caught at slip off Marcus North for 75 shortly before lunch. It was Strauss's second half-century of the match.
Trott showed admirable composure on a pitch which held few terrors after 15 wickets had tumbled for 243 on Friday.
He drove the ball handsomely through the off-side reaching his 50 in the morning session from 89 balls.
After Matt Prior had run himself out for four, Andrew Flintoff came to the wicket to a standing ovation in his last test innings.
He struck four quick boundaries but was caught at long-off for 22 trying to hit North out of the ground. North, who took over the off-spinning duties after Australia omitted specialist Nathan Hauritz, took four for 98 from 30 overs.
Graeme Swann entertained the capacity crowd with nine boundaries in his 63 from 55 balls while Trott patiently acquired runs at the other end before he was finally out after striking 12 boundaries from 193 balls.
