Voltage drop in Vin of 7805 regulator when used with a Bridge rectifier and CT(Current Transformer)
The dropout of a 7805 is around 1.6V with no load, but this is not guaranteed you really need more voltage, but let's work with that. It also draws around 5mA with no output current. 

To reduce the ripple voltage to (say) 0.1V you need a capacitance of 0.01s*0.005A/0.1V= 500uF. Your 0.47uF is woefully inadequate, and your measurements are suspect because they have a shipload of ripple. 

That's assuming you have no other parts, however you have not entered your circuit schematic, so that's going to be it.