From D&D 3.5 to 5.0(5E) - 4 - Movement in Combat in 5th Edition Rules

In 5.0 your characters and your enemies will enjoy a little more freedom of movement.  The rules allow you to break up your move distance during your turn.  Thus you can move, attack, then move again.  A fighter with the Extra Attack feature and a speed of 25 could move 10 feet, make an attack, move another 10 feet and make another attack, and then move 5 more feet.  A Wild Elf with a speed of 35 could move 20 feet, cast a spell, then move another 15 feet.

Sticking with movements in 5 foot increments is recommended, especially if you are playing with minis on a grid.  But if your game is entirely verbal then you may feel free to tell the DM you are moving in 1 foot increments.  In either case, some affects are measured in 1 foot increments.  For example, if your character is crawling, for every 1 foot costs you an extra foot of movement.  Moving through difficult terrain also costs you one foot of movement for every foot you move.  Thus that Wild Elf with a speed of 35 could move 17 feet through difficult terrain, or perhaps 10 feet through difficult terrain followed by an attack, and then 15 feet of movement through normal terrain.

From D&D 3.5 to 5.0(5E) - 3 - Ability Scores and Subraces in 5th Edition Rules

Characters of all races get bonuses to their starting ability scores, and none get penalties.  Humans get +1 on each score.  Yes, you read that correctly.  Human PCs are no longer the baseline non-modified standard.  I believe Humans have more total starting bonuses than any other race in the PH.

The game also introduces "subraces" such as Mountain Dwarves and Hill Dwarves.  All Dwarves start with a +2 Constitution, but Hill Dwarves have +1 Wisdom while Mountain Dwarves have +2 strength.
Subraces also have some different proficiencies.  For example, all elves are proficient in the Perception skill, but only High Elves get the Cantrip ability which allows them to cast a Cantrip (0-level spell) even if the character has no spell caster class.  Wild elves may not get the Cantrip ability, but they do gain the "Fleet of Foot" proficiency which increases their base speed from 30 to 35.

From D&D 3.5 to 5.0(5E) - 2 - No More Base Attack Bonus (BAB) in 5th Edition Rules

The Base Attack Bonus (BAB) has been replaced by the simpler Proficiency Bonus.  High level rogues will no longer get additional attacks upon reaching certain levels, and may be limited to a single attack their entire career.  But that does not mean the party is over for everyone.  Fighters, for example, can acquire the ability to make two attacks in a round from the "Extra Attack" feat gained at 5th level.  Barbarians also can gain the "Extra Attack" feat at 5th level.  Fighters get another "Extra Attack" at 11th level, but Barbarians do not.

So your character sheets will no longer contain entries like +16/+11/+6/+1 for combat.  The bonus to your attack will be your Proficiency Bonus, which is +3 at 5th level.  Thus a 5th level Rogue will get one attack at +3 with any weapon he is proficient with, and a 5th level Fighter will get two attacks at 5th level, each attack getting his +3 Proficiency bonus as long as he attacks with a weapon he is proficient with.  When a character gets multiple attacks in a round, each attack has the same bonuses to hit.  Strength modifier (or dexterity modifier) + proficiency bonus + the roll on the d20.  If your character attacks using a weapon he is not proficient with, you simply don’t apply the proficiency bonus.  There is no need to deduct anything for lack of proficiency with a weapon.
Are you worried about the lack of attacks for your high level rogue?  Don't be.  The reduced number of attacks is compensated for in other ways in 5.0.

From D&D 3.5 to 5.0(5E) - 1 - The Proficiency Bonus in 5th Edition Rules

I've been an avid D&D 3.5 player since the edition came out, but I really like what I am seeing in the 5.0 rules.  It looks to me like they have a lot of the flavor of the 3.5 game but with simplified mechanics.  I intend to post about many of these over the coming months.

The Proficiency Bonus
Many variables we used to track in 3.5 have been replaced by the single Proficiency Bonus in 5.0.  The Proficiency Bonus is based solely on your character level and is the same for all classes.  What makes each class, race, and character different is the things that the proficiency bonus applies to.

There is no Base Attack Bonus (BAB) in 5.0, nor increase in each Saving Throw Bonus per level, nor skill points to assign each level.  Instead, when making attacks, rolling saves, and using skills you simply apply your Proficiency Bonus, if you have a Proficiency Bonus for that action.

For example, both rogues and fighters are proficient with short swords, and thus each will have the same proficiency bonus with that weapon at the same level.  This happens to be a +2 for a first level character and +3 for a 5th level character.  Both 5th level fighters and 5th level rogues have +3 Proficiency Bonuses on short swords.  Fighters however are more likely to have strength and feats that further boost their attack ability than rogues; so don't worry that your rogues will be as tough of fighters as your fighters.

As you gain levels, your proficiency bonus increases and that is it.  No more tracking base attack bonus (+11/+6/+1), instead it is simply your Proficiency Bonus.

Similarly for saving throws you don't need to modify bonuses to the three saving throw types when gaining levels.  Now you just apply your proficiency bonus to your save roll if your class allows you to apply your proficiency bonus to that type of save.  For example, clerics may apply their Proficiency Bonus to saves based on Wisdom or Charisma.  For dexterity saves they will likely never have a Proficiency Bonus, even at 15th or 20th level.