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"OH WATERS, TEEM WITH MEDICINE TO KEEP MY BODY SAFE FROM HARM, SO THAT I MAY LONG SEE THE SUN." - Rig Veda
There are a couple things to keep in mind when we read Biblical texts. The first is, we have to analyze what we are reading, when it was written, what genre it is, who the author is, and what is the main point of the text. (this means we are treating the Biblical text in the exact same manner we would treat any other ancient text).
Next, we look for parallels in the ancient world. Are there other similar occasions where lifespans are listed as being incredibly long? As it happens, the answer is actually yes. The most well-known example is the Sumerian King List
So we have examples of lists of important people with extroardinary numbers listed as their ages in multiple examples from the Ancient Near East. So there is a precedent for the Old Testament to do this.
Some scholars believe that the numbers are being used in a more symbolic way, rather than mathematically. The cultures of Mesopotamia were experts in numbers. They advanced a lot of key mathematical concepts that we still use today (including our division of time into units of 60). They actually discovered such things as logarithms, ad used mathematical ratios in their architecture. They also knew about the Pythagorean Theorem (you know, A2 + B2 = C2) and used it.
The Sumerians and other Mesopotamian peoples (since at least 3100 BC) used a sexagesimal numbering system, which means that it was base 60, instead of our base 10. Why? Because 60 is the lowest number divisible by all of 2, 3, 4, 5, and 6, making fractions much easier.
There were a lot of ambiguous things included in this numbering system, such as blank spaces possibly meaning zero, and less value put on the importance of position of the numbers (tens and hundreds place for example). Practically, this was not much of an issue for the scribes, because their numbers were always in a context that made them very interpretable (amounts of grain, weights of money, etc). Later scribes (such as Hebrews trying to interpret such numbers) would have a much more difficult time without the context.
The biggest issue with Mesopotamian numbers, however, is the idea of sacred numbers. Some numbers had a symbolic meaning beyond their mathematical meaning, and therefore were numerological rather than numerical in some contexts, meaning that its symbolic value would be used rather than its mathematical value.
Now, what connection does this have to the Biblical chronologies? The numbers are based on the Mesopotamian system of numbers. All the ages in the Genesis genealogies fall into two categories: numbers divisible by 5 (ending in 5 or 0), and multiples of 5 with the addition of 7 (or two 7s). 5 years = 60 months. The final digits are always 0, 7, 5, 2, and 9. 2 because 5+7 = 12, and 9 because 5+7+7 = 19. The odds are astronomical that there would not be a number in the list that did not match. Therefore, we have a lot of indications that these are symbolic numbers, based on a very different number system. We don't know what meaning these numbers may have had.
Additional evidence for these being symbolic rather than real can be seen in the fact that many of the patriarchs' ages overlap significantly, and impossibly according to the narrative. Additionally, there are different numbers among various ancient translations of the text (specifically the Hebrew Masoretic Text and the Greek translation of the Old Testament, the Septuagint).
Therefore, the numbers in Genesis are most likely symbolic of something we do not know, and are based on a numerical system established by the Sumerians, and eventually lost over time. Thus, the ancient traditions of the symbology were likely lost and the compilers of the Hebrew Bible themselves did not understand the symbology behind the ages.