I found the video on AppliancePartsPros.com extremely helpful. A lifesaver.
http://www.appliancepartspros.com/parts-for-whirlpool-ksm5.html
I disassembled the mixer (completely) and replaced the brush holders. My victim seemed to have the old-style holders. The brushes were damaged, so I replaced those, too. The Speed Control Plate was broken in half, so it got replaced. For a total of about $20 of parts the (nearly antique) hand-me-down mixer now works perfectly. A replacement mixer would have cost several hundred dollars.