Ric,
Try it. The 2nd floor of our house is 3 stories up in the rear. We do use the ladder and it can be a bit precarious, but it's a heck of a lot cheaper than buying the $600 power washer.
You can always buy the power washer afterwards. But the bug sprayer is a heck of a lot cheaper.
Remember to wear old clothes... the bleach can (and does) discolor what you wear.