I still haven't traced the tag line back all the way, but I was right. "The National Cancer Institute initiated the
national 5 A Day for Better Health Program to reduce cancer risk in America." (Monograph in PDF on the subject here.) It says it did so sometime in the 1980s, starting in California (which is a major producer of fruits and vegetables). In 1991, the program was rolled out nation-wide in the US by the fruit-and-veg lobby, operating under the name of Produce for Better Health Foundation.
WHO's own website begins its involvement in a 5 A Day campaign only in 2002. That was the same year the campaign began in the UK, under the NHS (NOT under the fruit and vegetable lobby).
I'm sure its history is more complicated than this. I do notice that the