Whirring noise with shutter release depressed

My Nikon D5500 (after approximately 750,000 exposures) has begun protesting its photographic regimen by merely making a high pitched whirring noise when the shutter release is pressed down. (No photos either…)

The first time it did this, I took off the lens to look inside, and managed to get the shutter assembly (mirror assembly?) to come unstuck. Took a couple more pictures, but then the mirror (and whatever else inside the camera) doesn’t seem to come unstuck now.

Any thoughts on what to expect to have to do to get this workhorse of a camera up and running again…? Or is it wiser to simply update to the D5600?