elk, you mentioned driving a standard 5-gear transmission in your car. That's exactly how I keep track of what gear to use on the bike. I don't know if this will work for you, but it definitely helped me to get used to gearing for hills.

When you're in low/easiest gear of the car, the stick shift is close to your body and the transmission runs in such a way that the car goes more slowly but you can more easily make it up hills. As you shift towards high/hardest gear, the stick shift moves away from your body, and the transmission allows the car to go faster, yet it has less power to get up hills.

The bike works the same way, only the stick shift= the bicycle chain and your body= the bike frame. When you're in lowest/easiest gear, the chain is close to the frame and you can spin more easily, which generally makes the bike move more slowly yet it's easier to get up hills. As you move into higher/harder gears, the chain moves away from the frame, and spinning becomes harder but the bike moves faster.

I'm not sure if I explained that well. Does it makes any sense? If it does, then basically the "number" of your gear becomes less meaningful because the direction in which the chain is moving is what helps you keep track of whether you're shifting in the right direction.