One of the best products for cleaning mold and mildew of of masonry or wood is the combination of TSP (trisodium phosphate) and bleach. You should be able to get a 1lb box of
Savogran TSP powder for around $5 at any hardware or paint store but who know with today's prices and still strange lack of availability. It may be a bit more but is still pretty inexpensive.
There are instructions on the box for how to combine with bleach. Just brush it on and leave it for a bit (don't let it dry). Scrub it off and hose it down. Always use good eye protection when scrubbing with bleach and also hosing it off. Stubborn stains may take more than one application.
There is certainly no harm in trying soap and some manual scrubbing to see if that works. One benefit of the TSP/bleach combination is that the bleach tends to kill the mold and spores so it takes longer to come back. Bleach also helps to lighten stains. If it doesn't look like it worked as well as you wanted it to, just leave if for at lest overnight. Sometimes it takes a bit for the bleach to finish doing its thing.
As mentioned, be cautions if using a power washer. They can do allot of damage in a hurry if you are not careful. They will shatter vinyl siding, break windows, and even take the bark right off of trees. Start on the lowest possible pressure setting and work your way up.
LMHmedchem