Mathematical approch to measuring current, voltage and resistance of mixed series and parallel
There is one important low-impedance node in the whole circuit. That's the frame and the cross in the middle. Let's call that 0v. The top voltage source is connected to the middle via that 1k resistor, that means the lower voltage source has priority.

The current flowing in:


the bottom resistor must therefore be 10v/1k = 10mA.
the right resistor must be 0mA, because it has the same voltage on both sides.
the two resistors in the top half form a potential divider between 0v and 0v, so you might think of the top voltage source as sitting at about 0v too. However, since it's generating a voltage, then the top side will be at 5v, and the bottom side at -5v.