The ages of the antediluvian patriarchs reported in Gen 5:5 (and later such details) allow scholars to date the creation of the universe, on one old theory, to 4004 B.C. This is called the “Young Earth” creation theory. Is this required by the text?

This is not a question to answer in a paragraph, but the short answer is “no.” There is nothing in the text that absolutely requires a Young Earth; there are several ways to avoid the conclusion. One is to say that the genealogies of Cain, Seth, and Noah leave many gaps. Another is that various people were lived before Adam and Eve, but they were specially created for life in the Garden, and were to become a special line of righteous people who could walk with God. Another, which does much more violence to a “literal” reading of the text, is the notion that the text must be regarded as repeating old, mythic stories that are true in metaphorical, symbolic, or moralistic senses, but are not strictly required by a respectful, “believing” reading of the text. Frankly, I do not think that any very important theological issues turn on which of these theories is correct. It is certainly true that the Bible-rooted Christian theology requires belief in miracles, prophesies, and divine manifestations; but it is less obviously true, to me, that the same theology requires belief in the precise names, ages, and events precisely as recorded in Gen 1-11.