Recently aquired a 68 with a 327 3 speed which had a stumble under light acceleration. Given that it sat a lot and knowing it acted like the accelerator pump, I rebuilt the Holley 4 barrel which made no difference. At this time I headed for electrical. Set the dwell and timing. The car has an Excel coil and external resistor and some ratty wires so I repaired them and checked voltage. It was under 5 volts. Thinking this is wrong I ran a jumper wire p bat to p coil. It has 12 volt key on but goes to 5 volt when running. Any ideas for the next test?

 

That is pretty much normal if you still using the point ignition. In this case when the ignition key is in the start position power to coil comes directly from the starter circuit. When the key is in the run position power to the coil is routed through a ballast resistor which drops the voltage down. This is done to prevent the points from burning as they can only constantly handle about 8 Volts. When the starter is engaged the battery voltage drops quite a bit, so the resistor is bypassed to allow higher voltage to the coil. The coil should work fine as it is designed to work at the lower voltage. If you are using electronic ignition then it always needs the full 12 Volts and the ballast resistor has to be bypassed. The ballast resistor could be an physical resistor or a resistor wire, depending on the car.

 

As I see it, you have a couple of things going on here. From the factory, the coil was supplied power through a resistor wire, not a separate ballast resistor, giving the coil about 10 volts to run on. Don't forget, that the alternator is putting out 14+ volts when the engine is running, and the resistance wire (and a ballast resistor) steps the incoming voltage down a certain percentage. So with a static engine not running test (12.? battery volts at rest), voltage at the coil wire should be even lower than 10 volts. If the original coil supply wire is still being used, and a ballast resistor added to that, then that's why you're getting a reading of only 5 volts with key on (not run). Check to see what voltage you have before the resistor, and if it's under 10, get rid of the resistor.
As Pete said, don't run the coil on 12 volts, you'll burn the points, and the Accel coil will do it faster than a stock coil will. I've tried it many years ago having a nifty clear distributor cap and an Accel coil, and it was like a violent lightning storm under there.
When checking voltage at the coil wire, disconnect it from the coil first. The 5 volts running reading you got, assuming that's the only wire on the + terminal, can't be trusted, as the operation of the coil and ignition can confuse a digital gauge.

 

Points closed, current flowing through coil, low voltage as resistance wire and/or resistor, reduces the voltage preventing point set from burning/eroding away, as 69 states.

Points open, no current flowing, battery voltage.
Yes, it is a lightening storm inside the dist cap.
As suggested, either OE resistive wire and stock coil, or Accel coil and ballast resistor with a new power wire from an IGN source, i.e., IGN spade on fuse panel.