If the solder melts the current is way too high - there must be a short somewhere. Either the 7905 is dead or the short is in the -5V circuitry.
The two resistors in parallel limit the current to less than 7V/10Ohm=.7A. Power over the Rs would be .35A*7V=2.45W each - too little to melt the solder. The voltage regulator must be dead (increases the power to .6A*12V=7.2W each - I guess the PSU maxes at 1A).
Remove the 7905 and check whether there's a short on the -5V track before replacing it.
