Kill it or Leave It?

The home we’ve recently moved into has this tree growing in the backyard. Short of decapitating dandelions I’m not much of a gardener but I’m a bit concerned about how close the tree is to the house. It is starting to lean a bit… pushing itself away from the house (not really obvious in the photo).

I would appreciate any suggestions in regards to what we should be doing here. Is the tree okay this close to the house? Should it be cut down? Or maybe just thinned out a bit.