Thank you for reply.
LED doesn't light at this current but it is working with lower currents just fine. It is true that the lamp is using 5A but I still think there is some power left even if transformer is overloaded. I think this is the reason why LED doesn't light.
However I changed the...
I have built a 5A version of this power supply. It seems it's working in some way but there is one 'load' problem. When I connect the 12V/60W lamp to PS and set both potentiometers to max. values I get around 11V at the output. This is somewhat strange so I think in theory this PS should burn...