Now is that 5 amp "max current" rms or peak? If it's rms you're exceeding 6 amps at times.
As a diode heats up, its voltage drop decreases. So the warmer diode may turn on at .65V and the cold one won't turn on till .75 volts. Thus whichever diode turns on first warms up and always switches on before the other, bears a disproportionately higher amount of current, which only makes it warmer still. That's why you can't share current between diodes without resistors which creates a large enough voltage drop to make the forward voltage variations due to heat and just mfg differences inconsequential. Unfortunately, they also make some heat, reduce efficiency, and add to the output impedance of the supply.
So it's really, really a good idea to start with a diode with the appropriate rating rather than trying to parallel diodes. Just don't do it, there's almost always another way.