We'll need to fix our notation in order to understand each other. Start by labeling nodes in the circuit as follows.
Node a connects R_1 and R_2.
Node b connects R_1, R_5, and R_4
Node c connects R_2, R_5, and R_3.
Node d connects R_3 and R_4.
Let the voltages at these nodes be v_a, v_b, v_c, and v_d. Since only potential differences are physically meaningful you can set any one of these equal to zero. Just so our notations match, let v_d=0.
Now you have to assume a direction for the currents through the resistors. Let the currents flow from top to bottom. Recalling that currents flow from higher potentials to lower ones, you should be able to write down expressions for the currents through the resistors in terms of the node voltages and resistances. Then you need to do the following.
1.) Apply KCL. There are only 2 nodes at which you can apply KCL, because you don't know the current flowing through the battery. So it should be easy to see where to do it. This will give you 2 equations, which is all you need.
2.) If the current i_5 through resistor R_5 is zero, then which two node voltages must be equal? This will eliminate one of the unknowns.
At this point you should be able to derive the result.
