Here's how The Umbrella Academy's Number 5 influenced the assassination of JFK within the show's mythology, and how the character ties into the real-life mysteries surrounding the infamous event. In The Umbrella Academy, Number 5 is blessed with the ability to make jumps through the time-space continuum and this power lands him to a job with the Commission, a shady group of time-travelers whose purpose is to ensure key historical events happen exactly when and how they are supposed to.
During his time with the Commission, Number 5 is constantly trying to find a way to jump back to his siblings and he achieves this goal in the middle of a mission related directly to the 1963 assassination of John F. Kennedy. Number 5 abruptly disappears through a time vortex before firing a single shot and, soon after, another gunshot is heard. It's unclear whether Number 5 was there to carry out the assassination himself, or was supposed to protect the President but abandoned his post and failed, and this leaves a number of question marks hanging over Number 5's role in the event, especially since the circumstances surrounding JFK's death remain a topic of much debate in real life.
While not explained on-screen, it is possible to deduce what transpired on that fateful day, at least in the world of The Umbrella Academy. In Gerard Way and Gabriel Ba's The Umbrella Academy comic books, Number 5 is indeed tasked with the assassination of JFK, forcing the Commission (known in the comics as Temps Aeternalis) to try and come up with another way of ensuring this pivotal event in human history takes place. While the story plays out very differently in the Netflix adaptation, the source material would seem to imply that the live-action version of Number 5 has been given the same mission.
In theory, Number 5 time jumping before shooting JFK should've meant that the Kennedy assassination was never carried out, but the President's tragic fate is subtly confirmed on-screen via the radio Number 5 was listening to in 1963, with the host announcing the death. This line is easy to miss without subtitles turned on. It must be assumed, therefore, that following Number 5's failure, the Commission sent another of their operatives back to the same time, but a different location, to ensure JFK's death happened as it was supposed to.
The consequences of these events aren't explored any further in The Umbrella Academy season 1, but the whole scenario actually fits perfectly into the real-life conspiracy theories surrounding JFK's murder. Official records show that Kennedy's assassin, Lee Harvey Oswald, fired from a nearby building, but testimony suggests a second gunman was present behind a fence on a grassy knoll that the President's motorcade drove past. The Umbrella Academy plays into this theory by suggesting that Number 5 is the infamous second gunman on the grassy knoll, while his Commission replacement carried out the actual assassination from the Texas School Book Depository building that Oswald was holed up in. Even though the Commission succeeded in their goal, it's fascinating to note that all of the rumor and mystery surrounding Kennedy's assassination was, according to The Umbrella Academy, caused by Number 5 time traveling at just the wrong moment.
The Umbrella Academy season 2 is currently in production at Netflix.