Yes, I’m that old. This is Marty Robbins singing “El Paso.” It was No. 1 on the Billboard singles chart on January … but let’s not be pedantic.
You can find out the No. 1 tune on the day you were born fairly easily. Just Google “No. 1 pop song March 21, 1965,” or whatever your date is. Wikipedia has the lists, year by year, week by week.