According to the Futurepedia, this is a special date in BTTF history, of course.
Saturday, November 5, 1955, is the date when "history is changed."
On November 5, 1955, Marty McFly used the DeLorean time machine to escape Libyan terrorists and accidentally traveled back in time to the very day Dr. Emmett L. Brown conceived of the possibility of time travel: Nov. 5, 1955. Where the Twin Pines Mall would someday stand, Marty arrived at the Twin Pines Ranch and crashed into Otis Peabody's barn.
Marty escaped gunshots and ran over one of the two pines at the entrance of the farm. Apparently, this caused the Mr. Peabody to rename his ranch as the "Lone Pine Ranch," and the mall to be renamed "Lone Pine Mall." (Those familiar with Joe Alexander's documentary will appreciate these details in terms of the 9/11 and Twin Towers metaphors.)
November 5, 1955, also was the day when, while hanging a clock in his home bathroom, Dr. Emmett Brown slipped and hit his head on the porcelain sink and had an epiphany: a vision of the flux capacitor, which he theorized could make time travel possible. He was only able to realize his dream after 30 years of toil and, in 1985, he built a time machine out of a DeLorean.
Stevenson has escaped to the future, but because he does not have the "non-return" key, the machine automatically returns to 1893. Herbert uses it to pursue Stevenson to November 5, 1979, where the machine has ended up on display at a museum in San Francisco.
Reasoning that Stevenson would need to exchange his British money, Herbert asks about him at various banks. At the Chartered Bank of London, he meets liberated employee Amy Robbins (Mary Steenburgen), who says she had directed Stevenson to the Hyatt Regency hotel.
Time machines, November 5th, Mary Steenburgen. Why does this show so familiar? Because in the BTTF franchise, we revisit all of this in the near future past of 1985, 1955, and 2015.
As one online forum exchange noted, the number 115 (specifically as 11/5, November 5th) is the day that Marty goes to in BTTF, as a time 1:15 is when Marty is to meet Doc (Marty gets there as the clock changes to 1:16...upside down 911).
The fact that November 5, 1979, turns up as the date of significance in the time travel of Time After Time is weirdly compelling.
Mary Steenburgen's character, Amy Robbins is the love interest of Malcolm McDowell's character, H. G. Wells. And because they met on the set of Time After Time, they would actually fall in love in their future, marry in 1990, have children, and divorce ten years later, in 1990. Where was Mary Steenburgen in 1990? Starring in Back to the Future Part III.
Mary Steenburgen/Clara Clayton would, in 1990, play Christopher Lloyd/Doc Brown's love interest in Back to the Future Part III. Steenburgen's father Maurice Steenburgen was train conductor who worked at the Missouri Pacific Railroad. In BTTF 3 Clara and Doc travel in a time machine made from a train, with 4-6-0 ten wheeler steam locomotive.
Mary Steenburgen would meet her next husband, Ted Danson, in 1993, when filming the 1994 Pontiac Moon, about the 1969 landing of Apollo 11 on the Moon. They were married in 1995.
See also George Barris, Batmobile Creator, Dies on BTTF Day [November 5th]