There are a number of things to consider:
The round ceramic resistor is bad.
One or both brushes are worn out.
The armature and/or stator windings are bad.
A wire connection is no longer connected.
The on-off switch is bad.
The control board has a fault.
Finding many replacement parts for for a K5-A is difficult but not impossible. The folks at WACEM may be able to help.
If you join WACEM (We Actually Collect Electric Mixers), you can find (under Files) the K5-A original service manual.
If the motor is working but the beater does not go round, it is most likely that the sacrificial worm follower gear has given out. These gears are essentially unchanged to the present day and are readily available. The Service Manual shows how to change it.
https://groups.yahoo.com/neo/groups/WACEM/info
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