When bad flight forced an early close, Australia, who had lost the toss, were 287 for three -- a marked contrast to their 60 all out in the first innings of their series-losing defeat in the fourth Test at Nottingham's Trent Bridge.
Smith, who will take over as Australia's Test captain when Michael Clarke retires following this match, was 78 not out after future vice-captain Warner had made 85.
A green-tinged pitch and overcast skies were reminiscent of conditions at Trent Bridge a fortnight ago where Stuart Broad took a devastating eight for 15 as Australia, likewise sent into bat by England captain Alastair Cook, collapsed in stunning style.
England went on to win 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.
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But today saw Chris Rogers, also retiring from international duty after this match, and fellow left-handed opener Warner put on 110 for the first wicket as Australia proved they could bat responsibly in typically English conditions.
"We knew it was going to be tough conditions, for us it was about leaving and respecting good deliveries.
"Me and Chris left well which put us in a great position."
Warner added: "To come out and show what we're made of was fantastic from our top order."
England all-rounder Ben Stokes said his side had been unlucky, telling BBC Radio: "We thought the pitch might have had more pace, but as a whole we bowled pretty well and might have had them five or six down on another day.
Broad was fractionally too wide early on against batsmen determined not to 'chase' the ball after their Nottingham nightmare.
The first hour's play saw Australia 19 without loss in 14 overs, compared to 38 for seven in 11 in 60 minutes at Trent Bridge.