I didn't think anyone but I remembered it. Ha! Did it come after 1970? Then the Internet remembers:
I had remembered it even nuttier than this, that the singers were counting to five and cheering, as if it were the most fun party game ever and maybe everyone was so loaded that they thought it was. Five! Whee!
The Muppet Wiki, which I had no idea covered Sesame Street non-Muppet activities, tells us that Jim Henson produced the bit, that it was written by Keith Vernon Textor and Alan Robert Scott. Which one wrote the lyrics? (Hyuk!)
It also appeared on a 1975 Sesame Street album called The Count Counts, "covered" by the "band" Three Bat Night.
I have to wonder where Textor and Scott came up with the melody. I just picture them writing it to be part of a song, maybe something like "My Love in the Dew" (it was 1971, and many songs had titles like that) and not being able to get anyone interested in it. "The heck with it, let's give it to Henson," they said, and the rest is history. Or maybe Textor did the melody alone and Scott did the animation. The Muppet Wikia is silent on many of these details. But we know there's a story behind everything, and often it's quite interesting, After all, Keith Textor was a professional musician from the 1950s, and wrote the theme song for Candid Camera, which was heard for many years on TV. The Internet is less forthcoming about Alan Robert Scott, his partner.
So if Messers Textor or Scott are out there and can weigh in on the origin of "1-2-3-4-5," please drop us a line at frederick_key at yahoo.com. The Internet has solved many mysteries, but we have to fill in the gaps. We're counting on you!