Application of Ohm's law to a single resistor and to a series circuit

For any given resistor following Ohm's law say a carbon resistor, it's resistance is independent of the value of current and voltage.

However, say we had a 5 ohm resistor in a circuit with a 10V battery. Ideally, the 10V potential would be dropped entirely across the resistor. This 10V potential is the work that would be done to move a 1C charge around the circuit by the definition of potential.

But, if say I connected another 5 ohm resistor in series with this, the drop across each resistor would reduce to 5V. How is it possible that for a given resistance whose value doesn't change (at relatively low current values) the work done to move a unit positive charge changes? After all resistance is the obstruction offered to the flow of current and hence the energy required to overcome this opposition for a given amount of charge should always be fixed?

What aspect of this reasoning is incorrect? The only thing I could thing of would be that we are dealing with potential energy instead of potential since that would make since due to varying current leading to a reduced amount of charge and hence reduced potential energy. But I'm pretty sure that goes against the definition.