The resistors only drop voltage because there is a current flowing through them.
If we have an open circuit, say the wire from the last resistor to the battery (EMF source) was disconnected. Measuring from the -ve terminal of the battery to the +ve terminal, using a voltmeter, we find 5 volts, at the junction of the two resistors we still find 5volts and at the disconnected end of the second resistor we still find 5 volts, because no current is flowing.
When we make the connection, current* can flow from the +ve terminal of the battery, through the first resistor, through the second resistor and back to the -ve terminal of the battery.
It is the same current which flows all the way around this circuit, there are no branches to the circuit, the same current flows in each element of the circuit.
If we use our voltmeter again, we measure 5v at the +ve terminal of the battery, 5v at the top of the first resistor, 2.5v at the junction of the two resistors, and 0v at the bottom of the second resistor.
This description assumes that our connecting wires are perfect and have zero resistance.
In the real world the wires will have resistance, so if we have a voltmeter with enough resolution we may see something like this:
At the +ve terminal of the battery 5.000volts
At the top of the first resistor 4.990 volts
At the junction of the two resistors 2.500 volts
At the bottom of the second resistor 0.010 volts
There is 0.01volts to drive the current through the resistance of the wire back to the battery!
Does this help?
JimB
* I am assuming conventional current flow and am not going to get into a p*****g contest about conventional current vs electron flow.