I think that he could be confusing animals with the five groups of vertebrates. IMAO, Is common in English to use animals mostly for big animals with bones and critters or bugs or "somethingsomething-fish" for everything else.
If we need to choose just five, among the really, really successful types of animals (in a very broad sense) we have Mollusca, Artropoda, Cnidaria, Chordata and... lets see, I would dobt between Platyhelminths because most vertebrates are hosts of several of them, or maybe Nematoda because they are hugely influential and everywhere in the soil in large amounts.
But we have also a lot of other groups: Annelida, Porifera, Echinodermata, Brachyopoda, Bryozoa, Priapulida etc... Definitely more than five big types of animals.