Five miles on a modest used road bike with smooth street tires at a moderate pace should take you about 25 minutes of riding each way, adding a few minutes for hills and traffic.

The same 5 miles on a used mountain bike with knobby tires, low gearing and energy-sapping suspension should take about 35-40 minutes each way.

I'm 62 and my current commute is 6 miles each way and it takes about 33 minutes (30 in, downhill...36 back, uphill). On my super-light aluminum & carbon road bike I average 28 minutes. On my big heavy, 90's MTB with studded snow tires it takes about 40 minutes, but with its summer smoothies and higher road gearing it averages about 36 minutes.

Recently, in 3-4 inches of fresh, heavy snow it took 48 minutes to get to work. And it took about 45 minutes on my horribly under-geared 16-inch folder (soon to be upgraded...I hope).

I have various routes, both streets and trails and a mix of both.

For 28-years I commuted 9 miles each way and it took 50% longer (about 45 minutes average).

I would say that if you are in reasonable shape, for a 5-mile commute, almost any bike would do, the only real variable being the amount of time you wish to spend riding.