The 5e Hack No One Asked for

Player Stuff

Ability Scores
Derivative ability scores are a sacred cow; it's time to take it to the slaughterhouse. 
Instead of rolling out ability scores, each character gets the standard array: +3, +2, +2, +1, 0, -1. 

Race 
I'm tired of my players picking outlandish races for a stat boost and/or power. I want a more grounded grimdark feel. Every character is assumed to be human. If you want to play a member of a certain race, it'll be for roleplay or lore purposes only.

Class
Class features remain unchanged for the most part. When a character receives an Ability Score Improvement, they pick an ability score and improve it by +1, up to a maximum of +5. Spellcasting and Hit Points are also changed (see below).

Proficiencies 
I don't need a Survival skill to tell me that the Barbarian might know a thing or two about wild plants. Skill proficiencies are axed. Classes are, instead, proficient with checks related to two ability scores. These are the same as the classes' Saving Throw proficiencies, as written in the book. Weapons, armor, and tool proficiencies remain unchanged.

Proficiency Die
Instead of a static bonus, PCs roll a proficiency die. Just multiply the static bonus by two and slap a "d" behind that number and you'll know which die to roll. If your class has Expertise, roll the die twice and take the better result.

Hit Points
Roll 4d6k3.
You can reroll any results less than your Constitution modifier once.
Add your hit die maximum to the result.
That's your HP for your entire career.
For example. Hrega the Terrible, a barbarian, has a con mod of +3. Her player rolls 1, 2, 4, 6. She rerolls the 1 and 2 and gets 3 and 1. Her result is 13. She adds 12 to that, because Barbarians have a hit die that's a d12, for a total of 25.

Spellcasting
The magic system is Alexandrian (Kempian? It's GLOG's!) in design.
5E has three different spell progression trees for some reason. 
Full spellcasters, like wizards, start with 1MD and gain 1MD every level up to a max of 10.
Half-spellcasters, like Rangers and Paladins, get their first MD at level 2 and gain 1MD every second level thereafter up to a max of 5. 
One-third spellcasters, like arcane tricksters and eldritch knights, get their first MD at level 3 and gain 1MD every third level thereafter up to a max of 3.
MD stands for Magic Dice. They're d6s.
When the spellcaster casts something, he chooses how many of his MD he wants to invest, then rolls. Dice with results 1—3 go back into the pool and ones with 5—6 are expended till the next rest.
If the spellcaster roll doubles, that's a mishap. If they roll triples, that's a calamity! (I ain't going to write specific mishaps and calamities for each class. That's what an imagination is for. All I need to know is that a mishap is inconvenient and a calamity is, well, cataclysmic.)
the number of [dice] involved as well as the [sum] of those dice determine the outcome of the spell.
Full spellcasters start with 3 spells, half start with 2, and thirds start with 1. They gain a spell every level, every second level, and every third level respectively. Other spells have to be discovered, researched, learned, and/or prayed for.
Clerical magic is more (?) reliable.
(whew! I think that about does it. Why is magic always a complicated affair?)

I just remembered that spellcasters have spellcasting ability modifiers so a Kempian magic system won't cut it. I'll probably use a DCC style casting system instead. The idea was to have one roll determine the success and outcome of the spell, but whatever. This game is about rolling to hit and rolling damage anyway.

Background
Ask of your character these questions three: What do they love the most? What do they fear the most? What do they hate the most? These answers three, their background be.

Monster Stuff

Hits
Monsters have hits, instead of hit points. A monster's number of hits is equal to its HD. When a PC hits a monster, the damage roll determines the number of hits lost.
natural 1: 0
2—5: 1
6—9: 2
10+: 4

Other Stuff

Surges
To offset the need for magical healing, each class can do a surge once per combat. A surge is an instant heal that restores Class HD + Level hit points. A first level barbarian would surge for 1d12+1 hit points. A sixth level rogue would surge for d8+6. (A fighter can do this twice with their Second Wind.)
PCs can roll surge for free while resting to restore that many hit points.

Dying
When a PC goes down, they roll their hit die. The result is how many rounds they have left until they bleed out and die, unless they're killed instantly by a hit that deals double their max hit points in damage. Each round the PC has a 5% chance to regain hit die hit points and re-enter the fray.

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I also wanted to try this thing from Index Card RPG where each area has a set Target Number. If that Goblin Warren has a TN of 14, you'd need to roll that to hit the goblins, disarm their traps, decipher their poo-scribbles, etc. Also allowed for modifers for hard and easy tasks, usually in the for of +/- 3—5.