After having a chance to play 13th Age for a while now, and having the chance to run Dungeons and Dragons 5th edition a few times now, I think some house rules have congealed in my head. If I were to run 5th edition again for any length of time (more on that later), I think these are the rules I'd have to use.
Alignment doesn't effect anything in 5th edition, as near as I can tell. Bonds, personality traits, ideals, and flaws all define the character, and work with the Inspiration mechanic to encourage role playing. Alignment is less important than ever in D&D.
Yeah, its traditional. Its also divisive and misapplied more than just about any other rule in D&D. 13th Age does a great job of feeling like a spiritual successor of D&D without alignment, so I'm pretty sure a D&D game can survive the excision.
I don't like playing on a grid. I have learned this in recent years. After having run 5th edition a few times, I have also learned I don't really want to keep track of exactly how far away people are from one another, and to have a bunch of running totals for character distances.
13th Age has a great tactical movement system that doesn't involve exact movements. Its not particularly difficult to translate "Far Away/Nearby/Engaged" into D&D. Precise movement rates are still useful for chases to help determine advantage or disadvantage.
13th Age has simplified weapons and its ranges already take into account the movement system, but I don't think it's too hard to convert ranges on the fly.
Abstract Ranged Attack Ranges
Since it takes a full round of movement to get "far away" using the 13th Age system, and given the average PC moves at 30, if a weapon or attack cannot be used at a range greater than 60 feet, it can't be used "far away."
If a weapon has a range greater than 60, but that range would put the attack at long range, then the attack from far away at disadvantage. If the entirety of the weapon's range is 60 feet or less, then a character doesn't need to worry about the weapon being at long range so long as they are attacking a nearby target.
Since D&D has it's own rules for disengaging, instead of the disengage check in 13th Age, a character would follow those rules to disengage.