No, it wont work. The net feedback is positive. If you exchange positive and negative opamp input, it should work.
But I cannot understand why adding a BJT. It just complicates the circuit.
The circuit will work if you remove the BJT and feed directly from opamp output to gate of mosfet. Dependent of type opamp, you can probably get rid of all resistors but load.
Also 5V voltage may be too low for the opamp to work properly. Also a negative voltage supply may be neccesary if your opamp doesn't have rail to rail output.