NMOS High Side switch circuit solving
You call this a switch, so the first thing to know is that to turn on a FET, Vgs should be greater than the threshold voltage.  

If it's a good switch the source will be close to 5V when on.  Therefore the gate voltage should be >Vth ABOVE 5V.  In your picture the gate is at 3.5V, so you DO NOT have a good switch.

There are a couple of ways to determine the voltage across the resistor.  You can use the FET equation with your resistor load (Info from here):


Or you can do it graphically with a load line on the output characteristic of your FET.  Your VDS is $$VDS = 5-Id*R$$ so plot that on the characteristic curve and see where the intersection point is.

Here's an example from Wikipedia for a bipolar transistor but the technique applies to FETs as well:



You could also simulate or use numerical methods or a MATHCAD or MATLAB model to figure it out.

If you are actually using the FET as a switch, then you can get a very good approximation by looking for the RDSon on the datasheet for the Vgs you are applying, and just considering the voltage divider formed by the on resistance and the load resistance.