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Just realized that in DMing 5e I have unconsciously used a falling-in-water rule-of-thumb that I inherited from somewhere (maybe 2e or AD&D or maybe even Pathfinder). The ruling I've been using is as follows:

  • No damage for 20 feet of falling.
  • Half-damage next 20 feet.
  • Normal damage beyond that.

Realizing there should be a Strength (Athletics) for "swimming" (in context, "diving") to take even less damage with a proper dive in sufficiently deep water, I started to look for specifics on that. Am I just missing it somewhere? (Also didn't find it searching this stack.)

Are there clear 5e rules for both jumping and diving in water of various depths?

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There are no rules for falling or diving into water in 5e at all

Right now, this is an area the rules don't touch on at all. It is left completely to the DM.

The only rules listed in any of the rule books for falling in any medium is the basic rule in the PHB and the optional rules for flying creatures and falling from great heights in XGE. Other than that, nothing else is mentioned about water or otherwise.

Jeremy Crawford confirms this and offers up a personal house rule in this tweet:

There's no official rule for falling into water. As DM, halving the falling damage is what I typically do.

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No, falling is falling

The rules on falling(Basic Rules, Chapter 8) don't specify differences of what you land on.

A fall from a great height is one of the most common hazards facing an adventurer. At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. The creature lands prone, unless it avoids taking damage from the fall.

Falling into water is no different than falling on land with regard to the rules. I'm not a fan of bringing real world physics into answers, but water not being compressible along with surface tension make falling onto water from great heights still quite dangerous.

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