1-5V to 4-20mA voltage drop problem
I think you completely mis-understand what a 4-20 mA loop is. 

In your circuit, even if you could get the current to 20 mA through the R1 resistor you could not drive an external loop Rx with it.
Most 4-20 mA loops use an external power supply for loop power and may have significant voltage drop in their Rx circuits and connecting wiring.

You should study devices such as this which produce an accurate loop current, though it's supply voltage for the op-amp is much higher than 5V:

  

Your circuit might work better like this, though the input voltage is 0.4 - 2.0 V for 4-20 mA:







simulate this circuit &ndash; Schematic created using CircuitLab

The FET has a very low VGS(th) and the output loop could only withstand a 12 V loop supply.