R-2R ladder D/A converter with mutilple non-zero inputs
Start by redrawing your circuit:


Draw a horizontal line for 5V power at the top of the circuit.
Draw a horizontal line for GND at the bottom of the circuit.
Move the resistors connected to 5V up and connect them to the 5V rail.
Same for the resistors connectd to 0V, but now down to ground.
Take a sheet of paper and cover the circuit.
Move the sheet right in such a way that only R1 and R2 show.
Calculate the node voltage of the sub-circuit.
Calculate the output impedance of the sub-circuit.
Knowing the node voltage and output impedance of sub-circuit R1-R2 move the sheet of paper right so R3 shows. 
Redo the calculation with the previous result and move R3 into the equation.
Repeat .. until all you have is a single resistor and a single voltage source for the ladder network.
Now finally take the opamp and its feedback resistor into account.


If you show your intermediate results in your question, people will be more than willing to help you along.