Yes you can.
The Ready action is what you're looking for. It's explained on p.192 192 of the player's handbook.Player's Handbook:
First, you decide what perceivable circumstance will trigger your reaction.
For you this would be, "If anything nasty comes towards me".
Then, you choose the action you will take in response to that trigger, or you choose to move up to your speed in response to it.
So your response would be, "I run in the opposite direction!"
So you use your action Ready to run and then, when a monster approaches you, you may use your reaction to move away. Generally you won't also be able to also Dash since that would require another action.