It depends on location, if you're biking in a city at rush hour you're stopping every other block, getting stuck behind other cyclists, and at least where I live, constantly slowing down to avoid getting killed by potholes. There's basically no way you're doing 5 miles in 20 minutes.

On the other hand, if you are in heavy traffic stopping constantly at lights other traffic is also going to be travelling at that same slow speed.

That's fair. I biked in San Diego last week and the lights/potholes were brutal.

You're claiming you can ride 5 miles in closer to 15 minutes than 20, and through a city?

If you commute you will mostly ride on dedicated bike lanes without many stops so you can go at full speed most of the way. I've commuted around 3 miles in a not so bike friendly city in Europe and it took about 15 minutes since there are dedicated bikeways without any traffic lights you can take most of the way.

If you commute in rush hour that is actually a lot faster than going by car, so biking is the fastest option available.

Edit: And that was at a leisurely pace, similar to the effort of walking.