Nobody who is driving today will ever see ubiquitous self-driving cars. You don't realize the deep connection between the automobile and drivers' need for autonomy. How closely the desire to own a car is tied to the desire to drive.
I own a car, but I've always hated driving. I value the freedom of having the ability to go anywhere, whenever I want. I also value my free time. I would trade the joy of attending to my 45 minute commute in the morning for the next episode/chapter of whatever in an instant. The desire to drive isn't a desire I share. I share the desire to get somewhere, which an autonomous vehicle will, pretty soon, achieve.
And the biggest problem with self-driving cars is that they don't really show their benefit until everybody's using them. A busy highway filled with a mixture of human-driven and machine-driven cars would make for a very enjoyable Michael Bay movie.
Actually, self driving cars will always have to deal with unpredictable behavior from neighboring vehicles. This will never change. They can react faster to other's wrong behaviors, evaluate and plan faster than human drivers, have greater knowledge of road conditions and environment, plus they don't get bored or inattentive. While they aren't up to the task yet, they are coming fast, because they have value for every driver who isn't just driving to drive.
I agree pervasiveness will be more than 5 years, but you'll be able to buy any car with an autonomous driver option in less than 20 years. In 5 years the first autonomous work vehicles will be on the road (specifically long haul trucking). Shortly after that someone will implement the autonomous traffic cop (red light camera on wheels), and traffic cops will be on their way out.