It's a difference over "is it right" vs. "will it work." As a licensed LV contractor, for you it needs to be right and nothing with that cable is right. My pragmatic take on it as a fat software guy closing in on 50 far too rapidly is "it's not right, but it may work anyway if you're willing to accept a slower speed as 'working.'"
I'd be astonished if that was thinner than 24AWG which is the minimum spec for Cat5. There aren't enough pairs for PoE anyway, so that's a moot point and I wouldn't recommend trying it anyway on an unknown cable. The twists look different to me (particularly the orange pair) so if two of the three usable pair actually are different that should be enough to avoid crosstalk. Technically you could run 10baseT over Cat3, so if 10MBit is defined as "working" then I'm pretty positive this could work.
It may be really dirty and utterly Not Right, but I have spit, electrical tape and a Leatherman and I'm not afraid to use them.