The top one will probably jump to the forefront of most Yankee fan's minds: Curtis Granderson's three-homer game against the Twins on April 19.
Not only did the Yankee leader in longballs belt a career (and team) best three home runs, he also added two singles to make it a perfect 5-5 night. He had 14 total bases and didn't record an out. It'll be tough for a teammate to surpass that this season. Despite the three homers and two singles, Grandy only recorded four RBI that night. Two of the long balls came off Anthony Swarzak while the third came off Jeff Gray.
The next two on the list both belong to Mark Teixeira. On April 21, he went 3-6 with two homers and a double during the Yanks historic 9-0 comeback in Fenway Park. The first was a solo shot in the sixth (off Felix Doubront) that seemed to make no difference, bringing the Yanks within eight. The next (off Matt Albers), a three-run shot from the other side of the plate, was considerably bigger, making it 9-8 in the seventh.
Tex's next feat of strength occurred on May 26 against Oakland, when he had four hits in five trips to the plate, including two home runs (off Bartolo Colon and Graham Godfrey).
The fourth and fifth best games are much tougher to determine. Six different Yankees have accumulated games with eight total bases. In chronological order: Eric Chavez, Nick Swisher, Raul Ibanez, A-Rod, Robinson Cano and Russell Martin.
I'll go with WPA (Win Probability Added) to break the tie. That means Martin, of all hitters, has the fourth best offensive game of the season. His 2-4, two homer game against the Mets nine days ago solidifies his spot here. He first brought the Yanks to within a run with a Yankee Stadium Special that hit the very top of the right field wall in the seventh inning off Jon Niese. He came to bat two innings later against Jon Rauch and launched a slider over the left field wall to walk off with a win and sweep over the Metropolitans.
No. 5 comes from none other than Ibanez, who, on May 8 against Tampa, had his own 2-4, two homer game. He broke a scoreless tie in the fourth with a two-run homer off James Shields. He then homered off Burke Badenhop to lead off the seventh to give the Yanks some breathing room (4-2).
The first game on the list isn't surprising given how good Grandy's been over the last year and a half. But 2-5 are, considering Tex has disappointed, somewhat, during the same time span, while Martin has a sub-.200 batting average and Ibanez has a sub-.300 OBP. It just shows that almost any player, no matter how good or bad, can surprise on a given day.