You can, providing the DM uses the initiative variant
Although there is no "Delay" action in 5e, there are a couple of Initiative Variants in the DMG, having a similar functionality.
When it's a side's turn, the members of that side can
act in any order they choose.
If the DM uses Side Initiative, players are free to choose their turn order every round.
Speed factor is an option for initiative that introduces more uncertainty into combat, at the cost of speed of play. Under this variant, the participants in a battle roll initiative each round.
If the DM uses Speed Factor, a player can't actually choose to delay their turn, but his initiative is being rerolled every round, and the player's actions affect its modifier.
See more details in DMG, Chapter 9, under "Combat Options" (page 270).