>> I need to build a PIC Circuit which will draw a total of 500mA,
>> and I need a transformerless PSU to convert 230VAC to 5VDC.
>
> At 500mA the power dissipatioj in the resistor will be 315 *
> 0.500A = 157 watts !!!!  (!!)
> This is not a practical way of getting 500mA at 5V from the mains!

What he said.

> A 3 VA transformer is small, cheap and much much safer.

You didn't specify why you wanted a "transformerless" design.  Perhaps
you'd be more interested in some of the somewhat new switching power
supply chips designed to operate directly from rectified AC wall power.
(ie Motorola/ONSemi MC333622)  By operating the transformer at high
frequencies, the physical size of the iron shrinks considerably - I
seem to recall an press release describing a 5V/1A supply that fit in
the space of a standard 3-prong plug...

BillW