Earlier quoted context omitted.
It's true that the cable says 5e on it but your device doesn't read the printed reading so it doesn't matter. That printed category tells you what was tested, not whether the cable works in practice. Which makes sense, but leads to the consequence I described.
Worthwhile to point out: The Cat5 cable required for gigabit Ethernet is merely twisted pairs with no insulation, which is pretty much a dumb basic cable (with 8 wires). That's why any cable can work in practice. I don't know how possible it is to find a really bad cable (untwisted) and it might work on a short length anyway. (Your 1980s office cabling must have been 8 wires if you were able to get gigabit later, so…
So yes, those cables though they weren't Cat 5e because it didn't exist when they were manufactured, also were not basic phone cables, and I believe when the building was formally opened it had "ground breaking" 10Mbit Ethernet to every laboratory.