
Dead branches held up in the canopy, gray and shedding bark, some of them large; limbs long enough to sweep the ground or the driveway; two or more trunks of similar diameter splitting from one low point, often with a seam of pinched bark between them; sprouts from the base and along the main limbs; a crown wider than the tree is tall with the weight out at the ends; branches crossing and rubbing wounds into each other. Foliage may look vigorous — this is a structure complaint, not a health complaint.
Not urgent
'Never pruned' is not a diagnosis. Forest trees are never pruned and do fine. What differs in a yard is that an open-grown tree builds a wide, heavy, low crown with no competition to correct it, and nobody removed the competing stem at year eight when it was a five-minute cut. So what you are looking at is accumulated correctable structure plus accumulated deadwood, and the actual risk usually narrows to one or two identifiable parts: a large dead limb over somewhere people stand, or a tight V-shaped union with included bark that will split under wind or ice.
Normally a tree trimming job: $250 to $1,400 around Indianapolis, depending on size and access. A range, not a quote.