Several possibilities.
Not sure of the most likely right off hand. It would be a lot easier if I were there.
Just going to throw some out and maybe you can determine the most likely according to how its set up.
First, the electronics in the control system needs voltage above a certain level at all times to work.
Your mechanic's meter shows the voltage over a certain scan period. Unless he is measuring it with a high speed Oscilloscope.
Ever see those huge capacitors car stereo systems have?
That is because the big amps will draw a huge amount of current almost instantaneously when a deep bass note hits.
And you cannot get enough power from the line fast enough to supply it.
So, its entirely possible that you are dropping the voltage on the system way below the minimum threshold for a few milliseconds when the amp makes a sudden draw.
Not long enough for his meter to see, but long enough for the computer to shut down.
Don't forget computers must start under certain conditions as to memory clearing, certain data lines at zero, that sort of thing.
So they all have a watchdog circuit that does a reset on the processor whenever you first start it up.
When the voltage goes below a certain point, the watchdog triggers a reset and restart of the processor, even though it might be able to keep going, because otherwise it might have corrupt data.
This will stretch out the dropout.
While the actual voltage drop might occur so fast that the engine would not have time to stumble, the reset takes long enough for a misfire or a complete shutdown for a few seconds.
Or, you are measureing the voltage at the battery, and its going too low at the computer.
If the computer or some other part of the ignition system shares a power buss with the amp, the voltage level on that buss might go way low without the battery ever seeing it.
Also, you could be overloading the ground.
You usually think of the ground as just being......well, ground. Its everywhere, sort like Chickenman.
But, its is a power line just like the hot wire. Just the other end.
And its made of steel instead of copper, so it has more resistance. The only reason you don't usually get problems with it, is because there is so much of it.
But, with sudden heavy current loads, it might not hold up.
If you are not coming directly off the battery with both the hot wire and a dedicated ground wire for your amp, that could be your problem.
The third reason, might be your choice of music.
Some K5s are hard rockers, but every so often you find one that likes the classical or easy listening...........
Think about your grandmother being forced to listen to Metallica.......