To dissipate 5W at 80 ohms, it would take 20V@250mA.
To dissipate 5W at 2 ohms, it would take 3V@1.6A.
Depending on what your power supply's power, output voltage, and output current and where the resistor is in the supply which might help you determine what it's supposed to do (for example, how far away it is from the AC input and the DC output), that might help you make an educated guess on what the resistor value is supposed to be.
But yeah I agree with you that the writing seems to say it's 80 ohms. On the other hand, it's rather strange for BOTH resistors to breakdown and read the same value. It's also strange that it reads two ohms intead of something much lower (due melted wiring which has shorted) or much higher (due to melted wire causing an open). In any case, if either of those happened you'd probably be able to see it and it would indicate something else failed causing the resistors to fail since resistors don't have much that can go wrong with them in the first place.
I'm rather inclined to think the resistors are supposed to be 2 ohms based on that reasoning, but I don't know anything else about your power supply so I can't make a guess based on the things I described above.
But I'm gonna guess that being power resistors, you found them near the output of supply. And 3V@1.6A seems more like something that would appear on the output of a supply than 20V@250mA. But I'm totally pulling that outta my ass.