The dryer is certainly not using very much of that power to run the fan. Most of it is being used to heat air. 5 kilowatts is more power than most toasters or microwave ovens use, so please be careful with how much of your hair or skin you expose to that hot-air blast. You could probably cook a meatloaf with it.
We are 8 light minutes from the sun. That means two things, we see the sun as it was 8 minutes ago, and we WOULD continue to see the sun for 8 minutes after it disappeared.