Why does the cable resistance jump from a low value to high value at a particular frequency?

Your tooling seems to be the cause there, not the cable. From https://www.keysight.com/main/editorial.jspx?cc=US&lc=eng&ckey=1428419&nid=-32775.536879654&id=1428419

The 4294A extends its measurement frequency range up to 110 MHz by terminating each measurement terminal with 50 ohm in order to eliminate the resonance of test leads (including leads inside the 4294A). The measurement discontinuity is caused by the change in termination impedance at 15 MHz when the ADAPTER is set to NONE or at 5 MHz when it is set to 1m or 2m. The measurement discontinuity can be removed by performing LOAD compensation.

Something as simple as a cable does not have discontinuities like that.

There may be a clue in the fact the problem occurs at a nice round number, 5MHz. Is this a place where your test set changes ranges? Maybe it changes output amplifier, or filter, and one of them is broken or damaged.

The fact that you've quoted measurements at 4.99MHz and 5.01MHz without listing them hints that you have more data hidden that might throw light on what's going on. Listing spot measurements at a few selected frequencies is fine when everything is behaving itself, but not when you're hunting for an anomaly. The detail of the response adjacent to 5MHz will be very valuable.

Please edit your question with a plot of all the data you have taken, which may allow us to make better guesses. A connection schematic to show exactly how the cable is connected to the analyser would be useful as well.