I think the fact that it is a United States Note is more significant than the fact it has a red seal. Your note is the 59,844,949th made in the series 1963 out of 63,360,000 total. The various issues of 1953 $5 USN's amounted to 264,440,000, whle the 1928's amounted to 879,394,789 notes. These were issued before and after President Kennedy, so I don't think he had much to do with them.
It was also the first and last $5 United States Note with the Motto, "IN GOD WE TRUST" -- Public Law 84-140 passed in 1956 mandated that the National Motto be printed on paper notes.