Washing is an important step. You don't need super high pressure to wash off dust or dirt. A small pressure washer with 800-1000 psi is enough. Stay back away from the siding or risk some damage. You can use a mild soap to help remove some stubborn deposits.
Priming depends on the type and condition of the existing paint. Old chalky paint and oil base paints need priming before painting. It is always a good idea to prime before applying the paint. This is the best way to know for sure you did your best.