Please clear up for me a doubt about the difference between two scriptures. The scriptures are, Genesis 46: 27 – which says 70 members and Jacob went to Egypt, and Acts 7: 14 – which says 75 members and Jacob were invited by Joseph. Who are those 75? Name them one by one. Who did not go to Egypt ? According to these two scriptures 5 persons did not go to Egypt. Name them one by one. I am enthusiastically waiting for your reply.
You can find the list of seventy in Genesis 46:27. I will let you write out the list for yourself. However, I might have a candidate for the five extra names (see below).
As for why Acts 17:14 mentions 75 people, I believe this is probably because the Septuagint translation of Genesis 46:27 has 75 rather than 70 going down into Egypt. Apparently, Paul (or perhaps Luke) followed the Septuagint on this one. Luke spoke Greek and probably was not even able to read Hebrew. The Old Testament used by the early church was the Greek Septuagint translation. Naturally, Luke quoted from this translation, as did most of the New Testament writers.
How did the change from 70 to 75 enter the Greek Septuagint translation? Did this happen at the time the translation was made, or were there Hebrew manuscripts with 75 in Genesis 46:27 before the Septuagint translation was made from the Hebrew? I do not know.
The next question is how the change from the original 70 to 75 who went down to Egypt. There are two possible reasons for this which make sense. The first possibility is a copying error. The copying of numbers in Hebrew is very easily subject to errors. The number system for the Jews was like Roman numerals. In other words, letters are used as numbers. Add to this the fact that some of the letters used as numbers are very similar. For this reason, copying errors were inevitable when Hebrew manuscripts were transcribed. They did not have copy machines back then! Therefore, we should be a bit careful to make too much about numbers in the Old Testament. The example you gave is not the only one in which, if we forget about the problem of copying numbers, we might be confused or might think there was some sort of error in the original. When you see an account of a battle in Judges and it says that 6000 soldiers died, you would do well to remember that this may have originally been 6600 or 600. I believe it is likely that the difference between 70 in Genesis 46 and 75 on Acts 17 is because of a simple copying error, either in the New Testament, or more likely in the Old Testament which crept in.
Does the fact that there are copying errors in the Hebrew and Greek text bring into question the inspiration of the Bible? I say no. It is the originals which are inspired, not the copies. God chose to use human beings, both to record the scripture, and to make copies. Also, translators are human. I suppose God could have miraculously moved the hands of all the thousands of copyists of the Greek and Hebrew texts, but he chose not to do so. I have studied this issue extensively, and have concluded that no important Christian doctrine or theological point is affected by the kinds of spelling, word-order and number-copying errors which have come into the Hebrew and Greek text. I say this because we can compare literally thousands of different Hebrew and Greek manuscripts of the Bible. We can compare the Masoretic Hebrew text of Isaiah from about AD 1000 to the Septuagint and the Dead Sea Scroll versions from about 200 BC, for example. The result is that the kinds of changes which have entered the text are truly minor.
There is a second possible explanation of the reason that the Septuagint translation of the Old Testament came to have 75 people mentioned as having gone down to Egypt. Scholars believe that the Septuagint count of 75 may come from the five sons of Ephraim mentioned in 1 Chronicles 7:14-21. Their names are Ashriel, Machir, Selophehad, Peresh and Shuthelah. This speculation may or man not be correct. The Jews at the time the Septuagint translation was made may have had access to information we do not have. We cannot be sure.
The question you raised is an example of the claim I made above that such errors are not significant. I do not see how the Christian message is affected in any way by the difference between 70 and 75 people who went down to Egypt. Add to this the fact that in modern times we have sufficient access to the manuscripts that in most cases we can decide which was the original. The evidence is strong that the original number in Genesis was 70, not 75, as almost all Hebrew texts have this. However, the means and reason that this was changed to 75 in the Septuagint is not certain. Whether this was a copying error or an adjustment done on purpose to take into account the other five sons, I am not sure. I hope this helps.
By the way, there is a third possibility, which is that the 75 in Acts 7:14 is the number of those invited to go down to Egypt, while the 70 in Genesis 46 is the ones who actually accepted the invitation and went down to Egypt. In this case, the five mentioned above from 1 Chronicles 7:14-21 may have been invited to go down to Egypt, but did not go with the rest of the family to Egypt. Acts 7:14 mentions those sent for, not those who actually went. This solution is a bit ad hoc, but I cannot eliminate it as a possible explanation. To me, it is more likely that Paul/Luke used the Septuagint. I am sorry to have more than one possible answer, but this is sometimes the case with such questions.