10Gb/s is not specced to run on Cat5e, though it should work over short distances.
Depending on the partial failure, you could see some (or lots of) dropped packets, a drop to 100Mb/s if one of the pairs not used by 100BASE-TX fails and both ends auto-negotiate nicely, or total failure of the link.
I don't think there's any provision for auto-negotiating to a lower data rate due to poor SNR.