This date was selected, (in my opinion) as an homage to the 1979 movie Time after Time, where H.G Wells pursues his best friend(who happens to be Jack the Ripper) to San Francisco on November 5th 1979. I have no proof to back this up, but it seems a very likely connection.

U.S. 1955 U.S.A. Chuck Berry Nov 12th, 1955 : Chuck Berry – popular for such hits as “Johnny B. Goode” and “Roll Over Beethoven” – is named by a Billboard poll as the most promising R&B artist of the year. He proved the pollsters right be becoming a huge success in more than one genre of music.

Based on http://www.thepeoplehistory.com/november12th.html.

This is too much for a coincidence ;)

According to another answer in this thread, Bob Gale's (co writer of Back To The Future) father was born on Nov. 5th, 1922. I just watched a documentary on youtube about a real life scientist (Ronald L. Mallett) whose father died in 1955 at age 33. This caused him to spend his entire life trying to figure out a way to travel through time to save his father. So that he would not be considered crazy, he disguised his work as research of black holes. I believe the Nov. 5th part is an homage to Bob Gale's father, while the 1955 is a tribute to the real life scientist's dream of traveling through time to save his father's life. I believe that this man's courage and determination to follow his dream played a major role in inspiring the story of one of the greatest movies of all time. Here is the link as my evidence. Skip ahead to 10:00.

After doing further research, I found a Huffington Post article written about the scientist (Ronald L. Mallett). Here is an excerpt:

How are you planning on spending this historic week?

During the “Back to the Future” week I’m going to look at some of my favorite time-travel movies which I have on DVD. Among them is the 1960 movie “The Time Machine” that starred the late Rod Taylor. In my opinion, this is the best and most accurate depiction of H.G. Wells’ novel. I love that movie. I will also watch the “Back to the Future” series. Incidentally, the first movie in the series has a special meaning for me because Marty McFly goes back to 1955, which is the year my father died. By the way, it’s also the year that Einstein died.

TL;DR. 1955 was chosen because it was exactly 30 years before the date that the screenplay was finalised. November 5th was chosen because it met the requirements of the script and the dates of filming.

1955

When Bob Gale completed the original first draft screenplay in February 1981, Marty's destination was March 2, 1952, anticipating a 1982 movie release.

MARTY: 1952?? This is 1952?!? Holy Shit!! You know what this means?? I’ve gone back in time 30 years! 30 goddamn years!!! I haven’t even been born yet!!!!

When the final draft screenplay was completed in 1984, the date of Marty's arrival in the past, anticipating a 1985 release date, was then shifted to 1955.

BROWN: Here's a red letter date in the history of science: March 19, 1955

Presumably if the film had been delayed a year or another draft written a year later, the date would have been shifted to 1956 and so on.

This fits nicely with a recent comment by the Bob Gale about 30 years being "a nice round number", allowing audiences to experience a significant narrative shift but without being too far into the past or the future to make it unlikely that characters would still be around.

Q. Why [did] you chose 2015 for second movie and not 2025 or any other year?

Gale: As Doc Brown said: "30 years. It's a nice round number." The first movie dealt with a 30 year period, so we felt it was appropriate to continue that motif in the sequels. Besides, Marty's kids needed to be the same age that Marty was in 1985, and 2015 was the perfect year for that.

_{^{'Back to the Future' fans #AskBobGale: Your toughest questions answered}}

November 5th

Gale claims that the date was chosen to fit in with the events of the script

Bob Gale: November 5 happens to be my father's birthday. My father, I think, believes to this day that this is a great homage to him. It was just the right day with the right day of the week to make the thing work with the script.

Bob Gale: We picked November because of the time of the year when we were shooting the movie, and of course to make sense that they would be having things like a school dance in school. We obviously couldn't have it take place in August, because there wouldn't have been any school.

_{^{Maker's Commentary: Disk 1}}

Presumably these events included a non-Prom related school dance (which excludes Feb-Aug), long bright sunlit days and an unseasonal thunderstorm. Having Marty spend a week in the past (Saturday 5th to Saturday 12th) gives him the opportunity to meet both his mother and father at the weekend before they spend a week at school with the dance on the following Saturday.