Also, note that power supplies are DC only. What they may do for short durations, has no bearing on the settings of the dials. Most supplies have a big fat capacitor at the output, so that the short-circuit current peaks extremely high for a brief moment (10s of microseconds?) before settling to its steady-state value (which may still take milliseconds). Peak currents like 100A!
This is why you cannot test LEDs with a bench supply set at, say, 10V and 20mA.
Well, you can, but you need to remember to use the power supply
as a current source. Whereas a voltage source delivers zero power into an
open circuit, a current source delivers zero power into a
short circuit. So for testing LEDs, you must always short the leads together (so the circuit is carrying, say, 0V and 20mA), connect to the LED, then un-short. Then short again when disconnecting, move to the next LED to test, and so on.
Loose cables have an inductance in the ballpark of 1 uH per meter of length, not at all a negligible amount -- that 1uH has a reactance of, say, 50 ohms at 8MHz, and 8MHz is right around the transition frequency of most jellybean op-amps, where supply sensitivity and risk of oscillation are greatest.
An electrolytic capacitor, placed at the load, has a dampening effect, which helps to counter this. That's why it's a good idea, or at least some smaller capacitors, but those could actually make things worse, too (1uH resonates with 0.1uF at 0.5MHz, and the impedance can be in the same risky range (>10s of ohms) if the Q factor is modest, which it probably will be using film or ceramic capacitors here).
So that's the technical explanation of why I worry about oscillation, it's quite plausible.
(Now that we know it probably was a power sequencing problem -- in effect, testing the op-amp's input diodes like an unfortunate LED! -- it probably wasn't oscillation after all. Good to know.
)
The other thing you can do, to prevent surge currents, is simply wire up everything with resistors! For powering op-amps, a series 10 ohms is more than enough, say. A kohm is even fine for setting the op-amp input voltage, and limits the 5V supply to a short circuit current of merely 5mA.
Tim