Lots of things can cause a servo to run away on a system 5. A bad servo amplifier board is one of them, but it's unlikely that the board went bad just by sitting idle. You also said that you zero-returned the machine, so it sounds like the servo ran OK for a little while, no?
Look inside the CNC cabinet for the main power supply. It will have several cables with white Molex connectors on them, and there will be two cables going to each of the circuit boards. These cables conduct power to all this boards, and the old 5Ms had a problem in this area. Look for "browning" of the white plastic on the Molex connectors. That's a sign that the connector is getting hot. Later 5Ms had gold plated pins on these connectors, and they don't seem to have this problem, but the nickel plated pins would corrode and then heat up, causing a loss of power to some of the boards. A power loss to the lower "B" board makes the pulse coders lose power, causing a servo runaway.
Another problem on the 5Ms comes from some square, black hybrid ICs on the "A" board. They're in the upper-left area of the board, and they have numbers like: A-PC03, or A-PC06. Any one of these hybrid ICs can fail, causing servo troubles. Replacing them is easy, but FINDING one is a real pain. If you can get the CNC to sit stable with the servos on for a little while, try tapping on each one lightly to see if you can get the servo to jump.
If you can't power up without the Z servo running away, try this: Pull the fuses on the back of the Z servo before powering up. If you have a larger motor on Z, there will be 3 cartridge fuses as well as 3 1.3A indicator fuses. The smaller motors just have 3 15A indicator fuses. With the fuses removed, you should be able to power up the CNC and get a "ready". If you then try to Jog the axis, it will alarm out (becuse of no power), but at least you can test the velocity command (VCMD) signal from the "A" Board to the servo. Use a voltmeter and look at the voltage on pin #1 on the velocity board. If it's about 0V, then try to step-jog Z a few thousanths back & forth and see if you see a very small voltage + or - on that Z axis VCMD signal. It should smoothly transition from a small + to a small - voltage as you step jog back and forth past zero. If the VCMD signal is anything other than about zero volts, you have a bad hybrid IC on the "A" Board. If it is about zero, and it behaves correctly with the step-jog test, then you're problem is on the Z servo somewhere.
If it's on the servo, be sure that you have all the voltages on the servo board. You should see check pins to test +5, +15 and -15v. Use check pin CH3 as a ground reference for your voltmeter. The Z servo gets it's power from the power supply on the X servo (through a ribbon cable), so be sure that's plugged in. Also, remove the board and see if any of the pins on the Molex connector has "pushed back" when installing the board. That's a common problem also.