Why a light cruiser with only six 5-inch guns is a poor capital-ship escort

Would a 4,500-to-6,000-ton cruiser with six 5-inch guns and carried torpedo boats make a good capital-ship escort?

Not with that light an armament. The carried torpedo boats are interesting, but the proposed ship lacks enough gunpower for its displacement and escort role.

Six 5-inch guns would be inadequate for a vessel of that size, especially when compared with existing light cruisers. Carrying torpedo boats could be useful, but does not solve the weak main armament. A serious dual-purpose escort would need far more 5-inch guns before the arrangement became viable. At least seven twin mounts would be a more credible starting point for the proposed role.