how do I replace the power cord on a k5-a # 58-58248?

In order to get to the power cord connections, the mixer needs to be substantially disassembled. This involves:

Removing the head from the base (stand), then --
taking off the rear cover, drip ring, planetary, the 9 screws holding the halves of the head together, separating the halves, removing the rear bearing housing ....

If you are comfortable doing the above, and a bit more, look up and join (free) WACEM where you can find the original Service Manual for the K-5A plus a bunch of photos of your era machine's interior.

You can also ask more questions there and get answers from knowledgeable folks.

John
October 2015

The general case is to first take it apart - then remove the existing cord - then fit the new cord.

Given that you have to ask how to do it then it's very probable that this sort of work is outside your experience - perhaps you could ask a friend or neighbour to show you how.

Good luck...
October 2015

Who makes it?

You don't say
October 2015