[javascript] How to make a promise from setTimeout

This is not a realworld problem, I'm just trying to understand how promises are created.

I need to understand how to make a promise for a function that returns nothing, like setTimeout.

Suppose I have:

function async(callback){ 
    setTimeout(function(){
        callback();
    }, 5000);
}

async(function(){
    console.log('async called back');
});

How do I create a promise that async can return after the setTimeout is ready to callback()?

I supposed wrapping it would take me somewhere:

function setTimeoutReturnPromise(){

    function promise(){}

    promise.prototype.then = function() {
        console.log('timed out');
    };

    setTimeout(function(){
        return ???
    },2000);


    return promise;
}

But I can't think beyond this.

const setTimeoutAsync = (cb, delay) =>
  new Promise((resolve) => {
    setTimeout(() => {
      resolve(cb());
    }, delay);
  });

We can pass custom 'cb fxn' like this one

This is not an answer to the original question. But, as an original question is not a real-world problem it should not be a problem. I tried to explain to a friend what are promises in JavaScript and the difference between promise and callback.

Code below serves as an explanation:

//very basic callback example using setTimeout
//function a is asynchronous function
//function b used as a callback
function a (callback){
    setTimeout (function(){
       console.log ('using callback:'); 
       let mockResponseData = '{"data": "something for callback"}'; 
       if (callback){
          callback (mockResponseData);
       }
    }, 2000);

} 

function b (dataJson) {
   let dataObject = JSON.parse (dataJson);
   console.log (dataObject.data);   
}

a (b);

//rewriting above code using Promise
//function c is asynchronous function
function c () {
   return new Promise(function (resolve, reject) {
     setTimeout (function(){
       console.log ('using promise:'); 
       let mockResponseData = '{"data": "something for promise"}'; 
       resolve(mockResponseData); 
    }, 2000);      
   }); 

}

c().then (b);

JsFiddle

Implementation:

// Promisify setTimeout
const pause = (ms, cb, ...args) =>
  new Promise((resolve, reject) => {
    setTimeout(async () => {
      try {
        resolve(await cb?.(...args))
      } catch (error) {
        reject(error)
      }
    }, ms)
  })

Tests:

// Test 1
pause(1000).then(() => console.log('called'))
// Test 2
pause(1000, (a, b, c) => [a, b, c], 1, 2, 3).then(value => console.log(value))
// Test 3
pause(1000, () => {
  throw Error('foo')
}).catch(error => console.error(error))