Thanks for your help, the fault begins to be more clear ...

Having no oscilloscope, I used spartan methods

1) connected a 12V fan pair: the voltage dropped to 3.5V, but the PSU ran
well
2) added another +12V fan pair, but connected to the +5V line: +12 line
raised to about 9, +5 to 4.80 ... ran with no troubles
3) added another small load on the +5V (47 Ohm) and everything shut
down ... The +5V line connected fans were motionless (too low voltage)
and no motion was noticed adding the 47 Ohm load.

So I must assume there's no voltage peak: the protection scheme could be
a "current sense" and gone wild ?

4) Retained the +12V line connected fans and the 47 Ohm load on the +5
Line (removed the fans on this line): starts ok
5) Tried to move the trimmer (which should adjust the +5V, very slowly)
and power up, with the aforesaid loads.
6) Until 4.59 on the +5 line ... ok
4.60-4.66 starts, lasts few seconds, then shuts off
4.66 starts-stops immediately

That trimmer is connected to two transistor and some diodes (the small
orange-glass-like ones, not the "usual" black ones.

So, I suspect the fault is in the protection circuit, generating a false
positive.

I think of removing the two transistors and identify them.
If some diode is a Zener, the only way I have to test is to desolder them
and build a small auxiliary circuit (diode-resistor), to check the
breakdown voltage.