That 2010/11 series ended in a 3-1 England victory with Cook scoring 766 runs, including three centuries, but since then it has been a tale of woe Down Under for England, with Australia winning 5-0, 4-0 and 4-0.
There is a growing belief, however, that inspirational captain Ben Stokes can stop the rot against an Australia side described as the worst since 2010 by former England bowler Stuart Broad.
"We'd be naive to say Australia aren't favourites," the 40-year-old Cook told reporters on Tuesday at the Oval as TNT Sports launched its coverage plan for the five-Test series.
"But the way this England side plays, you think they've got a really good chance. Look at the batting line-up, England's top seven.
"On their day, they score runs at a tempo and pace to knock Australia off their lines and lengths.
"Everyone who plays England knows if you're not on it every minute, they can change games in an hour or two."
Unlike Australia's top order following the retirement of David Warner, England's almost picks itself, and while opener Zak Crawley averages only 31 in Tests, Cook says his partnership with Ben Duckett gives England the ability to dictate matches.
Crawley and Duckett partnership key
"That's a big competitive advantage the way that England's top order can go hard," Cook, who was England's highest-ever Test run scorer and century maker when he retired, aged 33 in 2018, said.
"If you look at Australia, (Usman) Khawaja and (Marnus) Labuschagne and maybe one other, that's not a fearful top order in terms of getting on the front foot.
"I think Australia will be so respectful of Crawley and Duckett. Crawley's a different opening batter to what history says you need; very inconsistent and averages 30.
"But on his day, he plays innings which I don't think anyone else in the world can play at the top of the order. If he has three or four good days against bowling, which should suit him, he is a real danger.
"They're definitely fearful of him. An hour and a half of Duckett and Crawley playing well on a first morning, England build huge momentum."
Cook picking Pope ahead of Bethell
Cook, who will be part of TNT's coverage team, said England should stick with Ollie Pope rather than Jacob Bethell at three, despite Pope being replaced as vice-captain by Harry Brook.
"If you get rid of him now, I think that changes the whole dynamic of what they've built up over the last year, how settled they'll feel for that top seven," Cook said.
"Bethell's an incredible talent, but that's in white-ball cricket. I think it's a big gamble to go with him because if that doesn't work, you then go back to somebody you got rid of."
As in all Ashes series in Australia, England's big names will be targeted on and off the field, although Cook says winding up Stokes may be folly.
"They know what Stokes can do if you poke the bear," Cook said.
"I think if there's ever a player in England's history who Australia feared, you put Stokes in that category."
Cook also thinks the pressure will pile up on the hosts.
"If England are in the series after three games, the pressure switches massively to Australia. They don't want to be part of a team which loses the Ashes at home," he said.