I have a continuous signal 5V at 0.5A
Another 5V 4A
Which would be more appropriate to feed my arduino UNO
Depends - are you connecting much of anything else? If not, then 5V/0.5A is plenty, same as you get from the USB connection with a PC. Hack a USB cable and bring in power thru the USB connector, or connect to +5/Gnd on the power header. Don't get them swapped, you are past the reverse polarity diode at that point.
The Arduino board uses ~50mA on it's own, plus whatever you connect to it.