On 22, Smith was caught at cover, only for replays to show Green overstepped. Next ball, Smith slashed between wicketkeeper Alex Carey and Beau Webster at first slip.
Smith also top-edged Green over the slips when he had 30 and, on 34, miscued a pull that just evaded mid-on.
This latest horror show in Sydney comes at the end of an incredibly disappointing Ashes for Smith, continuing a poor run of form that began in the home summer.
After Smith made an astonishing 184 in the second Test against India at Edgbaston in July, his batting average stood at almost 59. Eight matches later, it has fallen to 42.
He has passed 50 only once in Australia. In the first Test he did not adapt to the large boundaries in Perth and was bounced out.
In the second Test in Brisbane, his first match with a pink ball, he missed two crucial chances behind the stumps. The 25-year-old’s 60 in the second innings of the third Test in Adelaide was his highest score of the series, yet he holed out off Mitchell Starc just as he was giving England hope of an unlikely run-chase.
Before the fifth Test in Sydney he was left out of England’s white-ball teams for the upcoming tour of Sri Lanka and the T20 World Cup that follows.
Smith still has the second-highest batting average for a gloveman that has kept in at least 20 Tests for England, but his collapse in form could leave a doubt over his place for the home summer.
“Jamie Smith is nowhere near the rhythm he should be,” said former England captain Michael Vaughan.
“This England team have to start to learn and accept. I read something that said Jamie Smith will probably get a pat on the back for trying to take the game on.
“That is the culture that is being created in this England side and that is why they have failed on this tour. There are times to get on the front foot but when it is so close to lunch and Marnus Labuschagne is bowling bouncers. I cannot accept that. It sums up this England side.”