From D&D 3.5 to 5.0(5E) - 20 - Dash Instead of Move/Move

Move/Move and Run are gone from the combat mechanics in 5.0.  As with most of the rule changes, the goal is to simplify the mechanics even at the cost of being less realistic in order to speed the game play.
Characters never, or perhaps very rarely, need to choose between a full round action, a standard action, and a move action, because in 5.0 you pretty much always get both:

• An Action
• A Move

If you want to move more than your move allows, then you are employing a "Dash".  So "Move/Move" in 3.5 basically equals "Dash" in 5.0.  This does not allow you to cover three times your movement distance on your turn.  If you choose to Dash action for your action, you gain the ability to move your movement distance.  So, if your movement is 30', the total distance you can move in a round is 60' (30' from your "move" and 30' more feat from choosing the "Dash" action).

There is no "Run", so your maximum movement is basically your movement times 2.

Don't forget, you can break up your move in 5th Edition mechanics.  So you can move 10', take your action, move another 10', take your bonus action (depending upon the bonus action), then move another 10' if your movement rate is 30' or better.