So here's something that should work as a 5V supply. I've run it in LTSpice and it shows < 3uV of noise at 5A output. Reality will push that up a bit with the reference being a big culprit.
You've got to have at least 2.5V above your output to regulate, but 3V is safer (like Kevin said).
I had to kill the current source feeding the reference, but that was driven more by the LT1021 (higher current requirements) and higher voltages and is not really necessary. I've run my GR78xx without the current source just fine.
Also, you might be able to get away with one LED (for D9/D12) depending on the OpAmp min supply voltage.
Hmmm... Less parts / smaller parts... could this fit on a smaller board