As a beginner, you are lacking a basic understanding of what you are trying to do and what you are measuring.
1. Your voltmeter has a very high impedance, usually >10^7 ohms. Effectively this looks like an open circuit when measuring a voltage. When you use series resistors to drop a voltage, the voltage dropped across them is proportional to the current flowing through them. This proportionality is linear and is known as resistance, measured in ohms. What you have done is measured the voltage with no current flowing through them, so it will be the same as the voltage going into them. Attach the load and current will flow through them and the voltage will drop, with I*R volts dropped across the resistor.
In your case you have a source voltage of 39V and a requirement for 12V for the lamps. So you need to drop 27V across the resistor. I don't know what the current or power rating of the lamps are, but let's say 100mA is required for the lamps to glow brightly. This means that the resistor value needs to be 27/0.1 = 270 ohms (approximated by a couple of 120 ohms resistors in series).
2. An Ammeter is effectively an almost short circuit to a power supply. It is inserted in series with the power lead and measures the current flowing into a circuit. It has a very low resistance shunt to pass this current through.
If you connect an ammeter across a power supply you are effectively shorting it out and risk destroying the power supply and/or your ammeter. Do not simply stick in another higher fuse. You will probably destroy the transformer or it will catch fire. The fuse is there to protect equipment from idiots that do things like this. Yes you are drawing 5A of current. It is probably overheating the transformer as the core losses are very high in overload.
Your 1176 is operating when you don't short out the power supply (ie when you leave it alone). Then the PSU can do its job properly.
I'd suggest reading up on ohm's law (very basic beginner stuff) and also find out how your measuring equipment works and what you are measuring.
Put the original low current value fuse back in.