Don't use a 7805 as the voltage reference. They can vary quite a bit with temperature, input voltage, etc. You won't get a nice stable output. I'd suggest a TL431 as a basic precision reference. Of course you can do much better, but many power supplies depend on these. Create a basic shunt regulator (think zener regulator) after the 7805 with a few mA of current; the 7805 provides a stable enough voltage to ensure that the current through the TL431 is basically constant, providing good regulation. Your voltage reference will then be 2.5 V, not 5 V.
Don't forget some output capacitance. Don't go overboard. 100 uF is likely enough; 470 uF is a lot. You may need to put a few ohms in series with this capacitor for stability, since many regulators begin to misbehave with a purely capacitive load, and modern capacitors generally have much lower ESR than they did years ago. Without output capacitance, load regulation (response to changes in load) may be poor.
In testing you may see overshoot, ringing, or outright instability. You may be able to easily tame these problems with a small cap from the opamp output pin to the negative input pin. Testing will tell you how much capacitance if any. You can see and play with the effect of this capacitor in a simulator, but you can't determine the optimum value, since many real factors aren't accounted for, like the actual gain of your transistors, parasistics in PCB and wiring, and many other non-simulated variables.