Process: 5e, basically. Except that I would go further, and there would not be a single aspect of the core 3 not fully playtested. The full PHB, MM, and DMG would go live as playtest material before publication. Also, I’d get some new blood on the team.
Design: all these would be subject to feedback, obviously
similar to 5e, with some more hidden optional complexity (ie easy to ignore). The actual design of a lot of abilities would be, behind the curtain, like 4e Powers, but written out more like 5e fighter maneuvers or Star Wars saga force powers and starship maneuvers. “Make Attack. You also disarm the target if they’re holding a weapon. Blah blah.”
Rangers and Paladins would have choice between spells and maneuvers, and maneuvers would have simple enough options that you could just use the same few ones and not think too much about it if that is what you want.
Casting focuses would have small secondary benefits when used, making them meaningful choices. Different casters would have different focus proficiencies. Less complex than weapon chart, since casters are generally more complex.
Warlock would have a build in the phb that is stone simple, like a Hexblade with less moving parts. “You’re an at will blast spammer, and nothing good will come of you.”
More caster classes would have unique spells. Full casters would have greater difference in what their cantrips do, and half casters would have more unique and evocative spells, as well as spells that tie groups of classes/subclasses together, like all pet builds having spells that boost pets when cast.
Fewer spells would specify a creature as the target. Let people shoot doors.
Darkvision would treat Dim Light as Bright Light with no radius, but use a limited radius for Darkness as Dim Light.
Rules and advice for running a game with different basic assumptions, like worlds with more common magic items or where magic crafting tech is improving rather than all the best stuff being ancient, or worlds where no sentient race is considered born evil, etc would be in the DMG. Tool use in downtime would involve making checks more, with those checks determining degree or speed of success.
There would be feats for each class and major “build” (like the gish) that help give a decent flavor of that option without multiclassing, or round out a MC character. Still 5e style feats, though.
4e style monster and encounter building, with 5e bounded accuracy.
Cantrips and leveled spells that combine weapon attacks with magical effects in the PHB, available for all caster classes that get cantrips.
More fighting styles, available to more classes.