Here's a Greasemonkey / Tampermonkey script that'll run a stop watch until an edit reaches 5 minutes of age.  Give it a try and see what you think.  It might have bugs, but it's close enough for government work I think.  (That's a United States idiom meaning it's poor quality, but it works well enough.)  Bear in mind that it only works on new posts and post edits, not on comments.

	// ==UserScript==
	// @name        SE realtime dates
	// @namespace   http://stackapps.com/
	// @description show Stack Exchange timestamps as realtime counters
	// @include     /^https?:\/\/(\w+\.)?(stack(overflow|exchange|apps)|serverfault|superuser|askubuntu|onstartups|mathoverflow|mso)\.com\/.+/
	// @version     1
	// @grant       none
	// ==/UserScript==

	function setIntervalWithContext(code, delay, context) {
		return setInterval(function() {
			code.call(context);
		}, delay);
	}
	
	function startTimer(el) {
		if (!el.title) return;
		this.el = el;
		this.interval = setIntervalWithContext(function() {
			if (!this.el) return clearInterval(this.interval);
			var x = Math.round((new Date() - new Date(this.el.title.replace(' ','T'))) / 1000);
			if (x>299&&x<360) this.el.innerHTML = '5 mins ago';
			if (isNaN(x) || x > 299) return clearInterval(this.interval);
			var m = Math.floor(x / 60) % 60,
				s = Math.floor(x % 60),
				s = (s < 10) ? '0' + s : s;
			this.el.innerHTML = m+':'+s+' ago';
		}, 250, this);
		timers.push(this.interval);
	}
	
	function addTimers() {
		while (timers.length) {
			if (timers[0]) clearInterval(timers[0]);
			timers.splice(0,1);
		};
		var timestamps = document.getElementsByClassName('relativetime');
		for (var i=0; i<timestamps.length; i++) {
			var stopwatch = new startTimer(timestamps[i]);
		}
	}
	
	var timers = [];
	addTimers();
	addEventListener('click', function() { setTimeout(addTimers, 1000) }, true);