Increase setInterval time over time?

I'm using this code to run a function every x seconds as long as there are no mouse movements or keys pressed. How can I increase the timer with 2x the value for every round as long as there is no user activity and cap it at 300000?

This is what I have so far, but I guess I need to actually get my time variable into the the setInterval again as it's been updated.

var idleTime = 0;
var time = 5000;
$(document).ready(function () {
    // Zero the idle timer on mouse movement.
    $(this).on('mousemove', function (e) {
        idleTime = 0;
        time = 5000;
    });
    $(this).on('keypress', function (e) {
        idleTime = 0;
        time = 5000;
    });
    var idleInterval = setInterval(timerIncrement, time);
});

function timerIncrement() {
    idleTime = idleTime + 1;
    if (idleTime > 1) {
        time = time*2;
        if( time > 300000 ) { time = 300000; }
        refreshContent();
    }
}

I have modified your code to this, I think this is what you need see console after running (don't move your mouse it will reset timer),

var time = 5000;
var idleInterval;
$(document).ready(function () {
    
    idleInterval = setInterval(timerIncrement, time);
    
    $(this).on('mousemove', function (e) {
        idleTime = 0;
        time = 5000;
    	clearInterval(idleInterval);
    	idleInterval = setInterval(timerIncrement, time);
    });
    $(this).on('keypress', function (e) {
        idleTime = 0;
        time = 5000;
    	clearInterval(idleInterval);
    	idleInterval = setInterval(timerIncrement, time);
    });
});

function timerIncrement() {

    console.log('refreshContent is called after '+time+' milliseconds');
    refreshContent();

    time = time*2;
    if( time > 300000 ) { time = 300000; }
    clearInterval(idleInterval);
    idleInterval = setInterval(timerIncrement, time);
}	
function refreshContent()
{
    console.log('Stuffs you want to do when refresh content is called');
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>