The 10 Ohm resistor provides the base-emiter voltage for the 2N3055. As more current flows to the load through the resistor, the voltage between the base and emitter increases, increasing the amount of current flowing through the transistor.
Take 35V AC and rectify it to get about 50 VDC. Now, consider what happens when you try for an output of 1.2V at 5A. The transistor has to drop about (50V - 1.2V) or 48.8 V @ 5A or around 244 Watts. Somehow I don't see this turning out well.
I know, the numbers aren't exact. I didn't account for the 1.4V drop across the bridge rectifier and I didn't account for the current contributed by the voltage regulator but it's close enough to show that it isn't likely to work at low voltages.
At 30V it still won't work. (50-30) or 20V @ 5A is about 100 Watts. I don't think so. See Figure 1 and the following table where it talks about 1.52 deg C per Watt temperature increase:
http://www.onsemi.com/pub/Collateral/2N3055-D.PDFTake 100 W and see from Figure 1 that the case temperature can't be higher than about 48 deg C.
See Maximum Rating of 115W @ 25 deg C - that's a Maximum and it depends on the heatsink keeping the device at 25 deg C.
I probably messed up the thermal numbers but they are close enough. This thing isn't close to working.
In my view, the transformer is seriously over-voltage. Even then, it is good to have a tapped secondary so that lower voltages can be selected when lower output voltage is desired.