I grew up in a Baptist background, which definitely believed in a world-wide Flood about 5000 years ago (about 1000 years after the supposed biblical age of Noah). I did pursue research on this recently though, even though I was skeptical about the fantastic aspects of the Genesis flood.
If you mean a world-wide Flood about the time of 5000 years ago, there is absolutely not a scintilla of real evidence for that. In fact, there is no serious evidence of a world wide flood at any time.
Regarding the population bottleneck, it started around 100,000 years ago and ended 50,000 to 75,000 years ago. It is somewhat possible that a catastrophic regional flood could have happened around then. However, this would have been so early in human history, that there definitely were not sufficient tools to make anything much bigger than a relatively small boat.
That leaves an open question of the possibility of a large regional flood between 7600 years ago and 77,000 years ago. In the recent secular book, The History of the Ancient World, the author suggests in a sketchy way, that is possible that before 7000 BC, that there could have been a catastrophic regional flood from which the great flood myths (and the Genesis flood story) come from. If you look under Outburst Floods in Wikipedia, there are a few candidates, starting with evidence of major regional floods in the Red Sea somewhat after 69,000 years ago, following the Lake Toba event and subsequent drought. There is another theory about one that was around 16,000 years ago around the Black & Caspian Sea. That could have been late enough for it to be the source of the mythic flood accounts and Genesis account. There is another theory about a Black Sea Flood about 7600 years ago.
However, even at 7600 years ago, there was no evidence that boat-making (and the necessary tools to make an Ark), were advanced enough for a very large boat. It is even more impossible for the earlier dates. And since it would have had to be a regional flood, it doesn’t make much sense that representatives of all animals would have had to be on the boat, since dry land was not too far away. It’s not even clear if someone in a boat couldn’t have seen mountains during such floods. And other than around the population bottleneck, there is no sign of a huge drop in population
In summary, I believe that there could have been a large regional flood (on which the Gilgamesh and other mythic flood stories were based), but there is not any evidence of the fantastic aspects of the Genesis flood. However, like the Adam & Eve account, the Genesis flood account would have had to had a sizable dose of symbolism/allegory.