When I connect a multi meter across BC and AC I get the same reading, both show 5V, but isn't the resistor supposed to decrease the current/voltage?
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Many multimeter manufacturers have standardized their equivalent input resistance at ten MEGohms. Some precision voltmeters have much higher input resistance. But let's assume your multimeter looks like a 10M resistor:
You have a voltage divider, which means that \$V_m < 5V\$. But not much less. \$V_m\$ is what the multimeter will display.
You might use a 10V or 20V scale to display the 5V result: a 2V scale would over-range:
Since \$V_m = 4.9995\$ volts, the display resolution is too coarse to resolve the difference between 5.00000 and 4.9995
If your multimeter had better resolution, you should be able to see the drop.
The voltage dropped across the resistor is proportional to the current flowing through it; the constant of proportionality is the resistor's value: V = I*R. When the resistor does not have current through it, as when it is open circuited or connected to a multimeter which has an impedance orders of magnitude higher than 5k ohms, there will be no measurable voltage drop across it.