You can pass it via an IIFE:
let x = 5;
const p = (x => new Promise((resolve, reject) => {
//         ^ use it here
  setTimeout(() => {
    resolve();
  }, 2000);
}).then(() => {
  console.log(x);
}))(x);
//  ^ pass it here
x = 3;
 
 
The reason this works is because we are creating a scope via our function which is binding a variable x as one of its arguments to whatever value is passed into the IIFE. 
This allows us to bind the global x to something else but the x bounded within the IIFE is unaffected.
Since we're using the same name both within the IIFE and outside of it, the inner x is also shadowing the outer one.
Maybe using different names would make things more readable:
let x = 5;
const p = (y => new Promise((resolve, reject) => {
//         ^ use it here under a different name
  setTimeout(() => {
    resolve();
  }, 2000);
}).then(() => {
  console.log(y);
}))(x);
//  ^ pass it here
x = 3;
 
 
Note: the above works because we're dealing with primitive values, which in JavaScript are immutable and thus a new one is re-created on each re-assignment.
var a = 'a'; 
var b = a; // this will bind `b` to the copy of value of `a` 
a = 'changed'; // this won't affect `b`
console.log(a, b); // 'changed', 'a'
 
 
If we were dealing with objects, using an IIFE wouldn't work:
let x = { changed: false };
const p = (y => new Promise((resolve, reject) => {
//         ^ still points to the same object as x
  setTimeout(() => {
    resolve();
  }, 2000);
}).then(() => {
  console.log(y);
}))(x);
x.changed = true; // this will affect y as well
 
 
The reason is that objects aren't immutable and thus each bound variable is pointing to the same object.
var a = { name: 'a' }; 
var b = a; // this will bind `b` to the value of `a` (not copy)
a.name = 'changed'; // this will also change `b`
console.log(a.name, b.name); // 'changed', 'changed'
 
 
In order to achieve what you need with objects, you'll have to mimic what the JS engine does with primitives and clone the object 
when passing it into the IIFE:
let x = {
  changed: false
};
const p = (y => new Promise((resolve, reject) => {
  setTimeout(() => {
    resolve();
  }, 2000);
}).then(() => {
  console.log(y);
}))({ ...x });
//  ^^^^^^^^ clone x when passing in
x.changed = true; // now this only affects the original, not the clone
 
 
Or using Object.assign:
let x = {
  changed: false
};
const p = (y => new Promise((resolve, reject) => {
  setTimeout(() => {
    resolve();
  }, 2000);
}).then(() => {
  console.log(y);
}))(Object.assign({}, x));
//  ^^^^^^^^^^^^^^^^^^^ clone x when passing in
x.changed = true; // now this only affects the original, not the clone
 
 
Note: Both object spread and Object.assign perform a shallow clone. For deep cloning, you can find many libraries on NPM.
See: What is the most efficient way to deep clone an object in JavaScript?
For most cases, this could also work:
let x = {
  changed: false
};
const p = (y => new Promise((resolve, reject) => {
  setTimeout(() => {
    resolve();
  }, 2000);
}).then(() => {
  console.log(y);
}))(JSON.parse(JSON.stringify(x)));
//  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ clone x when passing in
x.changed = true; // now this only affects the original, not the clone
 
 
Note: Using an IIFE is just a quick example. A regular function would work just as well (but still have the same issues for non-primitive values):
let x = 5;
const p = createPromise(x);
x = 3;
function createPromise(y) {
  return new Promise((resolve, reject) => {
    setTimeout(() => {
      resolve();
    }, 2000);
  }).then(() => {
    console.log(y);
  })
}