Threshold voltage of a pseudo nmos inverter
If we are looking for the voltage where Vin=Vout we can first assume (but we don't know it for sure) that MP is in the linear region. So we take the equation for the linear region (which I'm too lazy to type in) and set Vds to (5V-Vin) and Vgs to 5V.

Then we look at MN, since Vin=Vout it will be in saturation. Therefore we use the equation for saturation. We set Vgs to Vin. 

Since the drain current for both transistors is the same, we can equate the two expressions and solve for Vin.

In a final step we check our assumption, that MP is indeed in linear region.

Update:

If you want your hand calculation to match with your simulation you have to use a simpler model.

.model PMOS pmos (KP= 48e-6 VT0=-0.95)
.model NMOS nmos (KP=156e-6 VT0=0.7)




The text in blue is my "hand calculation" and it agrees perfectly.

Please note that due to the condition Vin = Vout I am allowed to connect the output to the input.