Rock Paper Scissors game – looking for guidance on adding rounds and DOM

Here’s my JS and HTML. I am wondering how I can add the playGame function to my playRound function so I can include rounds. Also, I want to display the winner of the game after 5 rounds without having to click one of my rock, paper, scissors buttons.

https://codepen.io/Reginald86/pen/GRLjpYZ

const rock = document.querySelector("#rock").addEventListener("click", function () {
let result = playRound("rock", getComputerChoice());
console.log(result);
});

const scissors = document.querySelector("#scissors").addEventListener("click", function () {
let result = playRound("scissors", getComputerChoice());
console.log(result);
});

const paper = document.querySelector("#paper").addEventListener("click", function () {
let result = playRound("paper", getComputerChoice());
console.log(result);
});



function getComputerChoice(){
  const choices = ["rock", "paper", "scissors"];
  let computerChoice = choices[Math.floor(Math.random() * 3)];
  return computerChoice;
}

const rounds = 5;
let playerScore = 0;
let computerScore = 0;

function playRound(playerSelection, computerSelection) {


  if(playerSelection === computerSelection) {
    return "It's a tie";
  } else if (
    (playerSelection === "rock" && computerSelection === "scissors") ||
    (playerSelection === "paper" && computerSelection === "rock") ||
    (playerSelection === "scissors" && computerSelection === "paper")
  )  {
    playerScore++;
    return `Player wins! ${playerSelection} beats ${computerSelection}`;
  } else {
    computerScore++;
    return `Computer wins! ${computerSelection} beats ${playerSelection}`;
  }
}


function playGame(){
  for(let i = 0; i < rounds; i++){
    if (playerScore > computerScore) {
    return "Player wins the game";
  } else if (computerScore > playerScore) {
     return "Computer wins the game"
    } else {
      return "Game ends in a tie"
    }
  }
}

Looking for guidance.