Does this circuit convert sinewaves to square waves?
Zener diode works as a normal diode in forward biasing and works as voltage regulator in reverse biasing.

Since the diodes used in your problem are ideal, you can consider them as short in forward bias and as voltage drop of \$ 5 \, \text{V}\$ in reverse bias.

So I think you should remove the voltage drop you made, replace it with a short circuit and the circuit will work but you should notice that it will produce square wave which has value of \$5\,\text{V}\$ in the first half cycle and value of \$-5\, \text{V}\$ in the second half cycle.

Adding a  generic diode for the output of your circuit will rectify the output signal and make the peak value to be zero in the second half cycle.