What happens if my first five cards are all action cards?

You can still play action cards that doesn’t require targets such as cards that allow you to draw a card, send a card from the deck to the graveyard, target an opponent’s unit, target an enemy hero etc. However, if all your action cards require a friendly unit on the field as a target, then you’ve just had what we call a “hard lock”. This happens when you can’t play any of your cards because there’s no valid target. Since you can’t play any card, you won’t be able to draw new cards. You’ll basically be an open target for your opponent to finish off without resistance.

Decks with high action card count (like Dante Resonate decks) or decks with action cards specifically targeting only their own units have a chance of encountering this, unless they have cards that allow them to target enemy units or other effects that allow them to play cards and draw new ones. In the example below, the enemy Chun-Li has been hard-locked. We can safely assume that she drew all 5 action cards at the first turn.