Because of all the recent discoveries of copies of ancient texts, many Christian apologists may be working with outdated numbers. From Clay Jones:
The bibliographical test examines manuscript reliability, and for more than a generation Christian apologists have employed it to substantiate the transmissional reliability of the New Testament. The bibliographical test compares the closeness of the New Testament’s oldest extant manuscripts to the date of its autographs (the original handwritten documents) and the sheer number of the New Testament’s extant manuscripts with the number and earliness of extant manuscripts or other ancient documents such as Homer, Aristotle, and Herodotus....
However, although apologists have stayed abreast of the dates of the earliest extant manuscripts and latest New Testament Greek manuscript counts, we haven’t kept up with the increasing numbers of manuscripts for other ancient authors that are recognized by classical scholars. For example, although apologists rightly claim that there are well over five thousand Greek manuscripts of the New Testament, they have reported the number of manuscripts for Homer’s Iliad to be 643, but the real number of Iliad manuscripts is actually 1,757.
Dr. Jones has attempted to bring the numbers up to date in this article posted at CRI. I’m sure they’ve changed even since the article was published, but his numbers should be close.
To learn more about textual criticism and the existing New Testament documents, I recommend this free course by Dan Wallace on iTunes U.