I've done a primer on how combat works in 5E with reference to earlier editions (primarily 3E and 4E). You can find it here: http://merricb.wordpress.com/2014/07/05/basic-dd-about-combat/
Of particular note as to differences:
* Bounded accuracy is greatly different from 3E
* Being able to move and make full attacks is very different from 3E - and moving between attacks? That's very new.
* Only movement provokes opportunity attacks, and only when you move out of an opponent's reach - you can run in circles around them all day long.
* The Special Manoeuvres of 3E: Grapple, Disarm and (especially) Trip are nowhere near as effective, if they exist at all.
* Cyclical Initiative is pretty much the same, though!
Cheers!
Of particular note as to differences:
* Bounded accuracy is greatly different from 3E
* Being able to move and make full attacks is very different from 3E - and moving between attacks? That's very new.
* Only movement provokes opportunity attacks, and only when you move out of an opponent's reach - you can run in circles around them all day long.
* The Special Manoeuvres of 3E: Grapple, Disarm and (especially) Trip are nowhere near as effective, if they exist at all.
* Cyclical Initiative is pretty much the same, though!
Cheers!