With two diodes back to back, the PIV never gets above 1.5V or so, so that's not an issue. Just make sure the current rating is adequate. Sometimes with high currents it makes sense to buy a bridge rectifier instead of trying to use individual diodes. You can wire it to drop voltage the way you want.
Having said that, I would use a power resistor instead. The current is more or less constant, so a resistor will work fine and won't introduce all of the switching noise of silicon diodes. R = V/I = (6.3-5)/3 = 0.43 ohm. If it's an old transformer meant for lower line voltage then you might need slightly more resistance to get down to 5V.