Extend linearity range of this opamp circuit
With a 5 ohm sense resistor and a 5 volt control signal you will get 1 amp through the load if the load's value of resistance is low enough. For instance, if the load is 10 ohms then you need 15 volts at the source of the MOSFET to drive 1 amp through 10 ohms plus 5 ohms.

Plus you need another 2 to 10 volts more on the gate to get enough conduction (generalism alert) through the MOSFET. So, given your values, even if the load was zero ohms, you will need a supply voltage that is at least 7 volts and more likely 10 to 15 volts. This assumes the op-amp output is rail-to-rail.

I will note that you have shown V2 as 1 volt and this could only ever push 200 mA through 5 ohms.I assume this is an error on your part as is not putting a ground symbol at the bottom of R1.