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, 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?