The "Big Five" is an industry nickname for the 5 large companies that own just about every publishing imprint in the United States. It used to be "The Big Six", but Random House and Penguin recently merged creating 'Penguin Random House'. So, even though as an illustrator you may aspire to someday work for Tor Books, you are technically working for MacMillan Publishing.
Not coincidentally, every one of the Big Five book publishers are based in New York City.
Recently, writer and data scientist, Ali Almossawi, compiled a chart of all the Publishers, and every one of their subsidiaries.
This chart is a wonderful opportunity for artists wanting to promote their work in the book market. Just think, nearly every one of these imprints has an Art Director with a need to hire a professional artist.