NodeJS and Webpack on Heroku - node.js

Question

I am simply trying to deploy a very straight forward nodejs server and webpack application to heroku but i get the following error from Heroku:
2018-03-26T12:02:19.952603+00:00 app[web.1]: webpack: Compiled successfully.
2018-03-26T11:52:19.406889+00:00 heroku[web.1]: Error R10 (Boot timeout) -> Web process failed to bind to $PORT within 60 seconds of launch
2018-03-26T11:52:19.406889+00:00 heroku[web.1]: Stopping process with SIGKILL
2018-03-26T11:52:19.486385+00:00 heroku[web.1]: Process exited with status 137
2018-03-26T11:52:19.497230+00:00 heroku[web.1]: State changed from starting to crashed
Seems like there is something wrong with the port but i am not sure what else i could do. Here is what my node looks like:
/* jshint esversion: 6 */
var express = require('express');
var path = require('path');
var serveStatic = require('serve-static');
app = express();
app.use(serveStatic(__dirname + "/dist"));
var port = process.env.PORT || 5000;
app.listen(port);
and my package.json:
{
"name": "xxx",
"version": "1.0.0",
"description": "xxxx",
"main": "index.html",
"scripts": {
"start": "npm run serve",
"serve": "webpack-dev-server --colors --watch --inline --progress --content-base /src --config config/webpack.dev.js",
"test:js": "eslint src/js/**",
"test:scss": "stylelint src/scss/**/*.scss",
"test": "npm run test:js && npm run test:scss",
"build": "npm run build:dev",
"build:dev": "ENV=dev webpack --config config/webpack.dev.js",
"build:prod": "npm run clean && ENV=prod webpack --config config/webpack.prod.js",
"clean": "rimraf -- dist",
"clean:all": "rimraf -- node_modules dist"
},
"license": "UNLICENSED",
"repository": {
"type": "git",
"url": "git+https://github.com/xxx/xxxx.git"
},
"keywords": [
"design",
"site",
"front-end"
],
"author": "xxxx",
"dependencies": {
...
},
"devDependencies": {
...
}
}