How Big5 get its name?

Ever wonder where did the name Big5 (character encoding method used in Taiwan, Hong Kong for traditional chinese characters) character set come from? Why not big6? Why not small5?
I didn't know the fact until I read an article stated in Sinchew press.
It is due to the original design goal to support the five major software packages used in Taiwan at the time, or to the five leading computer companies in Taiwan - Acer, MiTAC, JiaJia, Zero One, and FIC that collaborated to develop the code.