Not only eating and drinking, but all bodily pleasures, are prohibited on Yom Kippur. The Sages have listed five such afflictions: We are to abstain from eating, drinking, washing or anointing the body, wearing leather shoes, and marital relations.
These five afflictions correspond to the Five Books of the Torah which we accept without allowing our physical needs to intervene. They also correspond to the five senses with which man performs mitzvot and commits transgressions; to the five times the term nefesh [soul] is mentioned in the Yom Kippur Torah reading; to the five immersions of the Kohen Gadol on Yom Kippur when the Sanctuary stood; and to the five prayer services prescribed for the day: Ma'ariv, Shacharit, Musaf, Minchah, and Ne'ilah.
This is inaccurate in a few details. First, in the Mishnah (Yoma) it says eating and drinking are one affliction. Washing and anointing are two separate ones. Second, in the Mishnah it says no wearing of shoes (literally sandals but those were the shoes of the time); later this gets reinterpreted as not wearing leather as out ancestors moved to less hospitable climes. Third, the reason our sages emphasize the five is that the word afflict it affliction ענה is mentioned five times; five times it says afflict your soul so it does mention soul but the emphasis of our sages was on the word afflict.
Thank you for your notes. You are correct about the count and the source. Eating and drinking are considered one, and the focus is on the five mentions of affliction (Yoma 76a).
However, the Mishnah says "sandal". The definition of that term refers specifically to leather shoes. They had other footwear at the time, and the term "sandal" meant only the leather shoes they wore. See Shulchan Aruch Orach Chaim 614:2, Biur HaGra.
Also, this page is a quote from the Sefer Hatoda'ah by Rabbi Eliyahu Kitov. It is not something we can update.