Solving PMOS Analysis Problem
The usual practice in teaching MOSFETs is to make all the derivations for NMOS and say something like: "for PMOS it is very similar, just switch the nodes...". Then it takes a whole lot of time to understand the actual difference between PMOS and NMOS.

I tend to believe that this is your case: you do know how to solve problems with NMOSs, but you do not have much experience with PMOSs.

First of all, the transistor in the schematic seems to be wired incorrectly (as pointed out in one of the comments). 

Secondly, the current equation for PMOS in saturation is:

$$I_{SD}=K \times \frac{W}{L} \times (V_{SG}-|V_T|)^2$$

Substituting:

$$I_{SD}=250 \times 10^{-6} \times (V_S-0.714-1)^2$$

(note that \$V_G=0.714V\$ according to my calculations).

The current should also satisfy:

$$I_{SD}= \frac{5-V_S}{1200}$$

Equating the above two and solving for \$V_S\$ yields:

$$V_S=3.75V$$

We must also check that saturation condition holds (in order to justify our a-priory assumption):

$$V_{SG}=V_S-V_G=3.75-0.714=3.036V&gt;|V_T|$$

and

$$V_{SD}=V_S-V_D=3.75-(-5+4000\times I_{SD})=4.59V&gt;V_{SG}-|V_T|$$

Both conditions hold therefore PMOS is conducting and in saturation.

I suppose you might have been using a more sophisticated MOSFET model for Spice simulation, therefore the answer you got there is different (although pretty close).