The question was mostly answered already but I'm going to go ahead and post quotes from the 5e Player's Handbook itself as well.
Quote:
Your Turn
On your turn, you can move a distance up to your speed and take one action. You decide whether to move first or take your action first. Your speed—sometimes called your walking speed—is noted on your character sheet.
The most common actions you can take are described in the “Actions in Combat” section later in this chapter. Many class features and other abilities provide additional options for your action. The “Movement and Position” section later in this chapter gives the rules for your move.
You can forgo moving, taking an action, or doing anything at all on your turn. If you can’t decide what to do on your turn, consider taking the Dodge or Ready action, as described in “Actions in Combat
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Actions In Combat
When you take your action on your turn, you can take one of the actions presented here, an action you gained from your class or a special feature, or an action that you improvise. Many monsters have action options of their own in their stat blocks.
When you describe an action not detailed elsewhere in the rules, the DM tells you whether that action is possible and what kind of roll you need to make, if any, to determine success or failure.
1. Attack
2. Cast A Spell
3. Dash
When you take the Dash action, you gain extra movement for the current turn. The increase equals your speed, after applying any modifiers. With a speed o f 30 feet, for example, you can move up to 60 feet on your turn if you dash.
Any increase or decrease to your speed changes this additional movement by the same amount. If your speed o f 30 feet is reduced to 15 feet, for instance, you can move up to 30 feet this turn if you dash.
4. Disengage
5. Dodge
6. Help
7. Hide
8. Search
9. Ready
10. Use An Object
As you can see its basically along the same lines as charging in 4e where you could use your move action as a move then your standard action to do the Charge. The difference being that Dash doesnt let you attack at the end of it. While similiar to the Run action of 4e, Run was a 'move action', whereas Dash is an 'standard action'.
This means that you couldn't do something like Disengage then dash away from the enemy unless something was granting your a bonus action, becuase both Disengage and Dash are your 'standard' actions.
By the way if you have any questions about the other actions as they appear in the PHB let me know and I'll type them up here as well.