A missionary wrote "is it true that in the Dead Sea Scrolls it is attested that the family of Jacob arrived in Egypt with 75 people (where the Torah says 70) and that the LXX (Septuagint) also has 75? Is the Torah wrong when it says "70"?"
In the Torah, there are three places where we learn that 70 people went to Egypt with Jacob -
Yet, in the LXX / Septuagint both Genesis 46:27 & Exodus 1:5 mention 75 descendants -- although Deuteronomy 10:22 in the LXX has 70.
Ergo in two places the LXX says 75, but in one it agrees with the Torah and says 70.
Which is right and which is wrong?
The Septuagint (LXX) was an early translation of the Torah (Five Books of Moses) into Greek. The LXX / Septuagint is first mentioned in the 2nd century BCE in the Letter of Aristeas. The letter states that King Ptolemy II Philadelphus (reigned 281-246 BCE) wrote to the Jewish authorities in Jerusalem demanding that a delegation of Rabbinic experts be sent to Alexandria in order to translates the five books of the Torah into Greek for inclusion in his library. The story eventually found its way into the Talmud (folio 9a of treatise M'gillah).
Ergo the ancient translation of the Torah into Greek was only that of the Torah (Prophets and Writings were not translated) -- and all three of mentions of Jacob's 70 descendants are found in the Torah.
Learned Jews have always studied the Torah in Hebrew, not in Greek. Translations might be used as study aids, or for people in exile who were less learned. . . Over time the Greek translations (which came to include the other books of the bible, but translations varied in good or poor quality and were by persons unknown) became corrupt. Jews stopped using them, although Christians continued to use them much longer.
What is today called the Septuagint (which is the entire Jewish bible in Greek) are translations into Greek from persons unknown at times unknown. There was no quality assurance and as a result they became heavily corrupted over time. By the 5th century the Christians gave up on the LXX / Septuagint because it was so corrupt -- so why people now are debating this is really interesting. The term "self-serving" comes to mind. Origen, an early church father (died 232 CE) tried to piece together a decent translation by putting 6 different versions side by side (called the Hexapla). Here is what HE says about how bad the Septuagint had become "we are forthwith to reject as spurious the copies in use in our Churches, and enjoin the brotherhood to put away the sacred books current among them, and to coax the Jews, and persuade them to give us copies which shall be untampered with, and free from forgery." Origen, A Letter from Origen to Africanus, Ante-Nicene Fathers, Volume 4.
There is also St. Jerome (early 5th century) who decided to re-translate from the Hebrew rather than rely on the Septuagint saying: "I was stimulated to undertake the task by the zeal of Origen, who blended (the Septuagint) with the old edition Theodotions translation."
But. . . . what of the Dead Sea Scrolls (DSS) -- they are 2000 years old and both 4QExodb and 4QGen-Exoda-Exoda say "75" and not "70."
Wouldn't the DSS attest to the fact that the Torah is wrong?
Just because something appears in a Dead Sea Scroll (DSS) copy does not mean it is perfect -- and that the Jews changed it some time after 2000 years ago. Jews have a mesorah, a method of transmission, of the Torah which has amazing accuracy for Torot (plural of Torah) from around the world.
It is far more likely that some scribe wrote a note in a margin about Ephraim and Menashe's descendants and that note made its way into some copies along the way (Greek and Hebrew). It seems likely that some (if not all) of the scrolls found in Qumran (DSS) were destined for burial (when a Jewish holy work cannot be repaired it must be buried ceremoniously). Often such documents were stored in a repository called a גְּנִיזָה (g'nizah) -- a word which comes from the Hebrew verb גנז meaning to hide away.
There are scroll fragments from Masada (contemporary with the DSS) and from (early 2nd century CE) that are even closer to the Masoretic Text (MT) -- today's bible -- than the DSS - virtually identical; thus, proving the antiquity of the MT.
The Dead Sea Scrolls should not sidetrack you -- much of what was found was stored in a "graveyard." There are scroll fragments from Masada (contemporary with the DSS) and from Wadi Murabit (early 2nd C. CE) that are even closer to the MT than the DSS - virtually identical; thus, proving the antiquity of the Hebrew bible we use today. Actually most of the DSS supports the MT, not the Septuagint - this includes the Great Isaiah Scroll.
We have another ancient witness to the number of 70 (not 75) -- and that is found in the history by Josephus entitled "The Antiquities of the Jews." Written in the 1st century CE it bears witness to the number in the Torah: 70.
"Jacob, encouraged by this dream, went on more cheerfully for Egypt, with his sons, and all belonging to them. Now they were in all seventy. . . If we add these, which are sixteen, to the fifty four, the aforementioned number  is completed"
"As for Jacob, he became well known to strangers also, by the greatness of that prosperity in which he lived, and left to his sons; who came into Egypt with no more than seventy souls; while you are now become above six hundred thousand.. . "
Josephus, writing 2000 years ago (about the same age as the DSS 4QExodb and 4QGen-Exoda, wrote 70 -- although 4QExodb and 4QGen-Exoda have 75. `Both are 2000 years old, yet Josephus agrees with the Torah while 4QExodb and 4QGen-Exoda don't.
Most of the DSS do in fact "match" our modern texts. Those that don't follow the Hebrew (these would be the 4 Greek manuscript fragments that date to around 200 CE), come from cave 4.
Cave 4 is where the texts were not preserved carefully in jars indicating they were not considered as important. Archeologists have surmised that they were damaged texts or simply not important and thus weren't stored in jars.
Both 4QExodb and 4QGen-Exoda were found in Cave 4.
Given the amazing accuracy of Torah transmission, the reference from Josephus of 2000 years ago, and what we know of Cave 4 it seems highly likely that the Torah is accurate and 4QExodb and 4QGen-Exoda both contained errors.