Apparently Oliver Cowdery initially thought “drink of the bread” was a mistake, so he crossed out bread. But then he probably noticed the preceding verb eat, so he restored the word bread by supralinear insertion. Here “eat and drink of the bread and the waters of life” is to be treated as a respective construction—that is, eat is associated with bread and drink with waters. As would be expected, the academic word respective(ly) does not occur in the Book of Mormon text. The same kind of respective distribution in a conjunct structure occurs twice in another passage later in the text:
In the King James Bible, on the other hand, we have only fully separated conjunctiveness in phrases like “eat bread and drink water” (15 times), “eat flesh and drink blood (5 times), “eat bread and drink wine” (5 times), and “eat flesh and drink wine” (2 times). The Book of Mormon will retain the clearly intended conjunctive structures that must be treated as respective constructions: “eat and drink of the bread and waters of life” in Alma 5:34 and “eat(eth) and drink(eth) (of ) my flesh and blood” twice in 3 Nephi 18:29. Another example of respective usage is found in Moroni 9:8: “and the husbands and fathers of those women and children they have slain”.
Summary: Maintain the respectively distributed “eat and drink of the bread and waters of life” in Alma 5:34 (and similar instances of respective distribution in 3 Nephi 18:29 and Moroni 9:8); such usage is clearly intended.