There are early Mesopotamian texts also reporting kings of very great age. Is it not likely that the Bible got the notion of superannuated patriarchs from that source (Gen 5:5)?

Perhaps, or all such lists have a common source or sources. The famous Sumerian King List, found in multiple copies such as a tablet from Larsa and the Weld-Blundell Prism, name some eight kings (similar to the number of pre-Noachian generations) with ridiculously long reigns such as 28,800 years and 64,800 years. There is even a flood recorded, after which the reign lengths shorten, and then shorten some more (see Gen 11). What seems likely is that, given the number of extant copies of this list, it was even more widespread in the time of Moses, and so the highly literate author of Gen 5 would probably be familiar with such lists. Such lists are doubtless reflected in the genealogy of Cain (Gen 4) and of Table of Nations (Gen 10). If indeed elements of the Gen 1-11 narratives are mythic, they might have the notion of superannuated patriarchs from that source, or from a common source (see general questions about Genesis, above). Of course, it is possible that early man was simply long-lived, and God simply changed the laws of nature (see above), but even this suggestion faces issues in terms of reconciliation with scientific (especially anthropological and archaeological) discoveries.