UPDATED

As requirement, author is asking to keep playerSelection and computerSelection params for playRound. I'd propose the fix is to put playerChoice and computerChoice in while loop

let computerPlay = () => {
      let compChoices = ["rock", "paper", "scissors"]; //array storing computer possible actions
      let i = Math.floor(Math.random() * 3);
      let choice = compChoices[i];
    
      return choice;
    };
    
    let playRound = (playerSelection, computerSelection) => {
      let winner = "";
      if (playerSelection === computerSelection) {
        winner = "tie";
      } else if (playerSelection > computerSelection) {
        winner = "player";
      } else {
        winner = "computer";
      }
    
      return console.log(winner);
    };
    
    let i = 0;
    while (i < 5) {
      //here is the change
      let playerChoice = prompt("Select your action").toLowerCase();
      let computerChoice = computerPlay();
      playRound(playerChoice, computerChoice);
      i++;
    }

OLD ANSWER

Your problem is you pass prompt outside of your playRound. playerSelection and computerSelection should be in playRound too that would help for resetting values of computer and your choices' every round.

let computerPlay = () => {
      let compChoices = ["rock", "paper", "scissors"]; //array storing computer possible actions
      let i = Math.floor(Math.random() * 3);
      let choice = compChoices[i];
    
      return choice;
    };
    
    let playRound = () => {
      let playerSelection = prompt("Select your action").toLowerCase();
      let computerSelection = computerPlay();
      let winner = "";
      if (playerSelection === computerSelection) {
        winner = "tie";
      } else if (playerSelection > computerSelection) {
        winner = "player";
      } else {
        winner = "computer";
      }
    
      return console.log(winner);
    };
    
    let i = 0;
    while (i < 5) {
      playRound();
      i++;
    }