Australia v England 1894-95
This was only the second five-match rubber (after 1884-85), and "the first great Test series", according to the title of David Frith's book. England won the first Test after following on, and the second by 94 runs - but Australia fought back with huge wins in Adelaide and Sydney, setting up a decider in Melbourne. Needing 297 to clinch the rubber, England were 28 for 2 before Yorkshireman Jack Brown hurtled to 50 in 28 minutes - and 100 in 95 - to steer his side to a 3-2 victory.
Australia v West Indies 1960-61
This series had it all: a tie, a win for both sides, and a thriller in which Australia's last pair survived for 100 minutes to stave off defeat. The rubber that revived Test cricket after a drab decade hinged on the final match, in Melbourne: Richie Benaud's Australians scraped home by two wickets to pilfer the series 2-1.
England v South Africa 1998
After a soggy draw and a conclusive win at Lord's, South Africa were denied another victory at Old Trafford by England's tail, with the last pair hanging on for 7.1 overs. England, spearheaded by Darren Gough and Angus Fraser, bounced back with victories at Trent Bridge and Headingley (by just 23 runs) to steal the rubber.
India v England 1984-85
When India won the first Test, some feared a repeat of the yawn-making 1981-82 series, when a first-up victory for India had been followed by five boring draws on shirtfront pitches. But England bounced back, winning the second Test, then taking the lead in the fourth in Madras, after double-centuries from Graeme Fowler and Mike Gatting, and 11 wickets from the persistent Neil Foster. Both sides batted long in the drawn final Test, leaving England 2-1 winners after coming from behind, something they repeated in 2012-13... and possibly will in 2014?
Australia v England 1936-37
Don Bradman's tenure as captain started with two defeats, as Australia were caught on two rain-affected pitches. He made a duck in both games, too. England must have been worried about the backlash... and it came in the form of 270 in Melbourne (Australia won by 365 runs), 212 in Adelaide (won by 148 runs) and 169 back in Melbourne (won by an innings and 200). This remains the only five-match series won by a team that had been 2-0 down.
England v West Indies 1963
After three Tests, Frank Worrell's star-studded West Indian side had won one (by ten wickets), drawn one (the thriller at Lord's, which went down to the last ball) and lost one (Fred Trueman taking 12 wickets). But they pulled away with convincing wins in the final two Tests, the menacing Charlie Griffith taking nine wickets in each of them.
India v West Indies 1974-75
After Clive Lloyd's new-look side took a 2-0 lead - Gordon Greenidge hit 93 and 107 on debut in Bangalore, and Viv Richards 192 not out in Delhi - few gave the home side much chance. But, shrewdly marshalled by MAK Pataudi, they hit back with two fine victories, before a double-century from Lloyd set up the Bombay triumph that gave his side the series 3-2.
Australia v South Africa 1952-53
The authorities were so worried about a mismatch that serious consideration was given to calling the tour off. Favourites Australia duly won the first Test, but South Africa hit back in the second, their offspinner Hugh Tayfield taking 13 wickets. Australia won the third by an innings, but after a draw in Adelaide the South Africans - hailed as the finest fielding side yet seen - held their nerve to win in Melbourne and draw the series.
India v Pakistan 1986-87
These two neighbours/rivals had previously contested two series in which all five matches were drawn, and a repeat looked on the cards after four high-scoring but inconclusive encounters. But the pitch for the final Test in Bangalore offered unpredictable turn and bounce: Pakistan were shot out for 116, then India managed only 145. A better batting effort from Imran Khan's side left India 221 to win. It looked impossible - but Sunil Gavaskar, in what turned out to be his final Test innings, made a superb 96 (the next-best were Extras, with 27, and Mohammad Azharuddin with 26). But after 320 minutes Gavaskar finally was out to Iqbal Qasim, and India fell just short: it was Pakistan's first series win in India.
Australia v India 1977-78
In an entertaining series played concurrently with the first season of Kerry Packer's World Series Cricket breakaway, a second- or third-string Australian side - led by 39-year-old Bob Simpson, returning ten years after his initial retirement - won the first two Tests, the second by two wickets after a century from their nightwatchman, Tony "Rocket" Mann. But India hit back, their spinners taking 18 wickets in victories in Melbourne and Sydney (Bhagwath Chandrasekhar alone grabbed a dozen at the MCG), to set up a grand finale in Adelaide. Needing a towering 493, India got tantalisingly close thanks to a fine team effort - the highest score was Mohinder Amarnath's 86 - but ended up 45 short as Australia stole the series 3-2.
England v Australia 2005
And finally, the series Wisden dubbed the greatest of all: the epic 2005 Ashes. Australia, after their then-customary win at Lord's, were within a whisker of going two up before England clinched that heart-stopping two-run victory at Edgbaston. Australia's last pair hung on for a draw at Old Trafford, then England squeaked ahead with another close-run thing - three wickets this time - at Trent Bridge. Australia had the upper hand at The Oval, but England held on, thanks to Kevin Pietersen's 158 and the weather (unusually, the rain inspired cheers from the home crowd), to take the series 2-1 and reclaim the Ashes after 16 long years.
Steven Lynch is the editor of the Wisden Guide to International Cricket 2014. Ask Steven is now on Facebook