If you have clay soil, then I would recommend growing the peonies in a slightly raised mound with plenty of compost, and manure to raise it about 4 inches before planting the peonies so they drain well.

On the north side of the house with sprinklers running three times a week sounds like a very poor place to plant peony. Would likely become a mildew growing site, with non blooming peonies. Al

With plenty of sun---they'll love it. Close to a sprinkler head....couldn't be the worse place unless you wish to kill them the first spring /summer.

It comes down to, if you wish to have your peonies flower then choose a spot where they receive adequate sun, adequate water, and adequate care---this means you have to prop them up when the flowering gets heavy.
If you cant do this.....then you have chosen the wrong plant.

Life is not a bowl of cherries....give them what they need....or look for something else.

I agree with Steve and Al, I'd plant them in the full sun portion of your south facing yard. Peonies will wilt during the hottest days of summer but will recover as soon as the sun goes down. I'm also zone 5 and have the vast majority of my peonies in full sun, they do great.