Australia were 82 without loss at lunch, with Rogers -- in his last Test before retirement -- 27 not out and fellow left-handed opener Warner 53 not out.
It was in marked contrast to Australia's 60 all out on the first morning of the fourth Test at Nottingham's Trent Bridge a fortnight earlier.
England went on to win that match by an innings and 78 runs, a victory that saw them regain the Ashes and take an unbeatable 3-1 lead in the five-match series.
But Rogers, one of the few Australia batsmen who had been willing to 'knuckle down' this series, and Warner were far more watchful on Thursday.
Meanwhile Stuart Broad, who took a sensational eight for 15 in Australia's first innings at Trent Bridge, was fractionally too wide against batsmen determined not to 'chase' the ball after their Nottingham nightmare.
Australia's first boundary of the innings did not arrive until Thursday's 15th over when the normally aggressive Warner -- who had faced 45 balls without a four -- pulled Ben Stokes through square leg.
Two balls later, Rogers added a four of his own by driving Stokes to the cover-point rope.
An increasingly assured Warner, gaining from time in the middle, went to a 76-ball fifty when he cover-drove fast bowler Steven Finn for his seventh four.
Australia, however, recalled all-rounder Mitchell Marsh after dropping his brother Shaun, a top-order batsman, while fast bowler Peter Siddle was selected for his first Test of the series in place of the injured Josh Hazlewood.
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