Ability Scores and basic Mechanics. 5th Edition D&D uses the classical D&D ability scores… and how, it uses the heck out of them.
Ability score modifiers are similar to 3.x going from 1 to 30 with penalties at 9 or lower and bonuses at 12 or higher. Each score has a single modifier or the ability socre -10 and cut in half.
Ability Checks are the meat and bones of all task resolution in 5th edition Basic D&D. Roll 1d20 and add your ability modifier to meet or beat a Difficulty class of 5 (easy) to 30(nearly impossible). Contests between two individuals simply pits the dice rolls against each other, nice and simple that.
Skills are simply an refinement and extension of ability checks. Each ability score has a small selection of very broad skills. If you are proficient in a skill you roll a d20 add the relevant ability modifier and add your proficiency bonus (which is a fixed score from +2 to +6 depending on level).
Passive checks exist which are simply a means of a DM secretly determining success of an action without the player rolling dice again and again or potentially being tipped off to something they shouldn’t be aware of. The example in the introduction center would have been better explained as an application of Passive Checks as opposed to a die roll by the player.
The means by which each ability score and related skills can be resolved is adequately explained.
The biggest change to me in 5th edition D&D is the nature of Saving Throws. Each ability score can be used to make a saving throw. One doesn’t “save vs wands” or make “reflex save” they would instead make a Dexterity Save. Each class gets to use it’s proficiency bonus to save made for two scores otherwise saves are pretty much straight ability checks.
A host of picky and minor bonuses and penalties modifying a wide range of actions is dropped from the game by a simple and elegant mechanic : Advantage and Disadvantaged. If a character would have an advantageous situation involving any ability check, skill check, saving throw, or hit roll two d20 are rolled and the higher roll is used. If a character is disadvantaged two dice are rolled and the lower of the two die rolls is used. No multiple dice or ever stacking mods ultimately it boils down to typical, advantaged or disadvantaged rolls.
The adventuring rules are pretty brief and without the detail a DM would likely see on their side of the table and a such a lot of the pertinent details are absent at this point. Rules are given about movement and time within the game that are self-consistent; a party must be moving slow to be stealthy, if moving at a fast pace there is a penalty to perception scores.
Resting in 5th edition is broken down into a Short Rest and a Long Rest. A short rest is at least an hour long (really… not that short by my book). After a short Rest any character can recover HP = Hit dice rolled + Con mod. A long rest is at least 8 hours long and all HP are regained. Damage doesn’t stick with characters for long in 5th edition D&D.
Between adventures characters spend downtime living a normal life and pay up their lifestyle expenses, craft items if so capable, practice their profession, researching, training, or recuperating. When recuperating a character can recover from debilitating injury, disease, or poison after three days of rest a save made be made to improves the save vs one such condition each day.
Criticisms and comments: I like that ability scores have been made far more important. The play experience between adventures played with 5th edition and say 2nd edition style rules will vary greatly as HP loss is very brief and easily recovered in 5th edition. 5th edition will very much play like an action movie where heroes shrug of “flesh wounds” and never suffer the consequences of their actions for long.