After answering this question about how deep can PCs go underwater, I started wondering how long can you keep swimming before you die. Here are the constraints:
You can breathe underwater (ex, via magic items or spells)
Your speed is 30 ft and you have no swim speed
You are diving straight down, and the water is deep enough to accommodate your travel
You are not benefiting from Adv/D.Adv beyond what Exhaustion grants you
You die only when you reach an Exhaustion level of 6
The RAW is strictly followed, note we are not trying to be simulationist
Asking for a 100% chance of death is typically not useful, and in this case it is intuitively not (a +30 minimum for Con save guarantees survival, but that isn't interesting because nobody can normally achieve that).
So, to be useful, how long can a creature swim according to the constraints above before they have a probability of death equal to 95% or greater?