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