Can one apply 5v to the output/FB pins of an LM2596-5 without causing harm?
Well I'll take a stab at this. I am not an authority on the matter, but by looking at the internal schematic you should do no harm to the LM2596.
The feedback pin connects to an op-amp that will have no supply voltage.
The output pin connects the the emitter of 3 bjts (which should also cause no issue).