An interesting conversation ensued, though, when I called Kitchenaid's customer support.
I started by saying that I knew Kitchenaid did not repair K5-A's, but I would appreciate them referring me to an independent repair center.
"What is the serial number on your mixer?" was their first question.
"I have no idea. I'm at my office, and besides you don't fix K5-A's, anyway. I just want the name of a service center."
"What state are you in?"
"New Mexico."
"There are no repair centers in New Mexico."
"I know that. That's why I'm calling you. Are there are any service centers anywhere in the United States or Canada?"
"What state do you want?"
"I don't care. FedEx ships to any state."
"What are some states near you?"
"There's Texas, Arizona, Colorado, Utah and Oklahoma." (Obviously unfamiliar with geography.)
I called the service center in Texas, got a similar, parallel universe response, but finally did glean that repair for the K5-A doesn't exist.
I then called Hobart, but no dice.
So, my choice is buying a new one (now made by Whirlpool, not Hobart) or perhaps buying a used one on ebay. If you know anyone who has a working K5-A for sale, let me know.

I seem to attract parallel universe conversations--I really should start carrying a tape recorder. I bought some groceries today and had an unusual exchange with the cashier.
The deal was 8 giant boxes of cereal (Cheerios, etc.) for $10. Watta deal! I also had a dollar-off coupon in my hand. An even better deal! I put all the groceries on the belt with my knife (my key-ring that holds my frequent shopper card). Suddenly I couldn't find my coupon.
I told the cashier I didn't know what happened to my coupon. He said that he found it on the box of cereal and handed me my knife. After everything was rung up, I asked him again if he had really found my coupon. Yes, he assured me. Then I opened my checkbook and there was the coupon. I held up my knife and explained to him the difference between a knife and a coupon. Sheesh.
I think I'll sit in a corner and suck my thumb; it's been a weird day.