Before spending £105, it’s worth confirming it really is the scale. Swap the dead scale’s plug with a working one at the DRO head. If the fault follows the scale, the scale is dead. If it stays on the same axis input, it’s the head or that input.
On the 4 vs 5 wire question: the basic signals are just +5 V, 0 V, A and B. The fifth wire on the Sino scales is normally the reference or index mark, and the shield sometimes counts as a wire too. Plenty of DRO heads never use the reference mark unless you use the “find ref” function. So a 4-wire scale isn’t necessarily useless, as long as it’s 5 V TTL with the same resolution as yours (most likely 5 µm). You’d need to rewire it to match the Sino plug pinout, and you’d lose the reference-mark function on that axis.
If you want plug-and-play, used Sino scales from scrapped mills come up fairly often. Check the length, the resolution and the connector type before buying. A slightly longer scale is fine too, as long as the body fits where the old one mounted.