You should dab a little bleach on the suspected mildew and if disapears you have mildew. If it is mildew you should wash with a product call JOMAX and used according to the directions it will not harm the paint.

full strength bleach can mark the surface and almost anything can wipe it off so that is not a good test.

Powerwashing with TSP will do the job

JoMax does a great job. Get it at Loz or HD. Follow directions - mix with water and bleach & spray on with a garden sprayer. Hose off a few minutes later.

The TSP alone will not remove mildew you need to have bleach to do that and anyway it has been found that TSP can actually promote mildew. It has phosphates in it and that is what was baned from laundry detergents because of causing algea blooms in rivers.

I was not saying to wash the entire house with straight bleach but just to a small spot to confirm if it is mildew as bleach by itself will not remove plain dirt.