Unfortunately, no. The voltage reference i.c. will need a supply higher than 5V.
Depending on the particular i.c. you use for the ampliffier it could need at least a little bit of negative, otherwise its output may not go low enough to cut off the transistor when it isn't needed.
However, you could put a diode, perhaps two, or perhaps a low voltage zener in series with the amplifier's output and the transistor's base. That should overcome the inability of the amplifier's output to go very close to 0V.
I expect that you will experiment a little to see what works for you.
Analog Devices, amongst others, make a 5V reference i.c., type REF02. It has an output accuracy of ±3%, and a minimum supply voltage of 7.
So, with a bit of expriment you may dispence with a negative supply, but you will need something higher than 5V for the reference i.c.
I will use fixed 5V from other circuit for voltage reference, so this is not the problem. I already have fixed 5V. So can I use this reference voltage for VCC also? How can I do that?
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