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The development of a 25 T superconducting magnet is usually envisioned with the use of an HTS insert coil. Previously, we reported the successful development of a 3 T coil in a 19 T background field based on BSCCO 2212 conductor. Here we report on the progress toward a larger 5 T insert with 38 mm free bore. The design is introduced, which calls for 2 stacks of double pancakes and an outer layer wound section, all electrically in series. Reacted conductor is used with insulated steel tapes as reinforcement. Results in terms of field dependence of the critical currents and stress tolerance are presented for both bare conductors and double pancakes. The latter are tested in a 19 T, 0.17 m cold bore, magnet assembly.