"Is the foundation sinking at various points from 5/8" to 1.5 inches serious for a home built on a hill in 1955?"

No way for us to know more than someone on site, especially from the little info offered. Have 2 more foundation companies inspect and maybe an engineer or 2.

Do you see evidence that the house had quit settling or is it continuing to move? Is the 1 1/2" settlement in one location or many? Any idea if other houses in the area suffer the same problem due to poor soils, ground water or similar? Pictures?

Thanks all, I'll ask the neighbor's next time I see them.

Since we're new to the house, I can't tell if it's ongoing or finished settling but we do have cracks coming off the corners of windows and the basement floor slopes slightly. The 1.5 inch drop is only in 1 or 2 places but close to an inch around them.
scheduled a couple more foundation contractors to come take a look. I'm going to assume I need to budget for it and put other remodeling plans out of my head for now. 😮‍💨