I realize connecting two different voltage sources in parallel is a contradiction (in an ideal circuit). But if I were to connect this in practice and measure the voltage across points A and B, what value of voltage would it show? And how much current would be sunk by the 5V battery? (Non ideal conditions)
That totaly depends on the internal resistors of the voltage sources.
Then you can use the superposition principle and calculate the voltage level on the top of the circuit.
So, if both internal resistors have the same value the voltage V_out would be 7.5V. With other resistor values the voltage can vary between 5V and 10V.
A lot depends on the power supplies involved.
You can't do this with theoretical ideal voltage sources since any voltage difference would lead to infinite circulating currents flowing from the higher voltage source into the lower voltage source.
In the real world the most likely scenarios are:
For most typical bench power supplies they can only source current and not sink current. For example if I try this with the bench power supplies I have in my lab setting both to the same voltage. The one with the slightly higher voltage provides all the current until it goes into current limit. The voltage falls slightly and both power supplies conduct. If I set them to noticeably different voltages the one set higher provides all the current and the other displays a fault. Only the higher voltage source provides any current to the load, if any exists. The lower voltage source sees the output voltage as top high already and provides no current.
Some power supplies really don't like to be connected in parallel however so check the manual, or with the manufacturer first. For example a crowbar circuit on the output of one power supply, for OVP, may cause very high currents to flow possibly resulting in the failure of one or both power supplies.
Some power supplies are designed to share current. One way is to provide some defined series resistance, though this is often simulated to avoid power loss. The other way is to provide a common current share signal between the power supples.