Big5 is a superset of US ASCII representing Chinese characters in 2 bytes. It is/was widely used in Taiwan, but is not ISO2022? compliant. Unless there is a compelling reason not to, Unicode should be used in the place of Big5.
See also: charsets(7), charset(1), ascii(7) and unicode(7).
In the corporate world, the Big 5 were the large accounting firms:
Whether Arthur Andersen should still be counted in the Big5 after the fallout from Enron is very dubious.