Relatively successful was slotting the cat5 jacket, cutting off two or three of the pairs, twisting/tying the remaining pair to the old wire, then sliding the jacket back over the join before wrapping in a conservative amount of electrical tape. You want the join to be similar width to the cable and preferably flexible.

I have a suspicion that pulling fishing line first is the right play if you can manage to connect it to the old wire. Flexible, very high tensile strength, small.