You don't want to reduce the current, you want to reduce the voltage but in any case the 7805 will overheat without a heatsink. The power it dissipates is the voltage across the input and output terminals multiplied by the current through it "(VIN - VOUT) / I" and there is nothing you can do to stop that. If you are providing 12V from the adapter and you want to take 1A from the 7805 it is producing (12-5)/1 = 7 Watts of heat. If you want to run a 7805 without a heat sink I would suggest you keep the dissipation below about 0.25W.
The best you can do without getting into complicated circuits is add a resistor in series with the adapter output. The resistor has to drop 12V down to the voltage needed at the input of the 7805 for it to remain capable of regulating 5V at it's output, in most cases they need around 3V overhead so you want 8V at the input pin. So the resistor has to drop 12V to 8V at 1A, Ohms law says R=V/I so you need (12-8)/1 = 4 Ohms. The resistor will get hot though, it is going to waste the heat that the 7805 would otherwise lose. It will dissipate VxI = 4 x 1 = 4 Watts so you need a resistor of 5W rating or higher to give it a safety margin.
Note that the resistor and regulator produce heat proportional to the current you draw, the calculations are for maximum current (1A) so in reality it may not get as hot as predicted.
Don't forget to add a capacitor across the input and ground pins of the 7805 as recommended on the data sheet, this is particularly important if you add the resistor.
Brian.