There are exterior house cleaners that work OK that are sold at Home Depot and Lowes that are considered safe to use around the house, but they don't always get the job done. I personally like Clorox Outdoor Cleaning Bleach with the green label. It's stronger then the blue label that is used for laundry. It will turn your clothes white, right away, and then eat through them so there will be holes after you do laundry. I just put it in a sprayer and soak everything.
For black mold and stronger issues, I'll use liquid Swimming Pool Shok. It's a higher percentage of bleach then the green label stuff, and the results are more significant. Really the only thing that works with rental houses!!!!
Funny thing about the bleach is that I expected it to kill off my lawn when I was spraying down an X pen before letting a puppy use it, but the grass actually looked greener to me a week later. It never died, and there was no sign of where I had sprayed it.