I received the T5 captain ability, and the T5 unlock projects are available.
But I did not receive the "Romulan Star Empire (Tier 5)" accolade, nor did I receive the final New Romulus story mission ("Secrets of the Ancients").
I have relogged the character multiple times, changed zones multiple times, logged in and out of other characters multiple times, restarted the client, and completed other missions and accolades in the meantime, but the Romulan T5 accolade has still not appeared.
A few days ago, when I completed Omega reputation T5, the accolade and associated mission contact (500 Omega marks, etc) did not appear until after I completed the project to receive the MACO Mk XII ship shield.
I do not have, and will not have for days or weeks, enough Romulan marks to buy anything I want from them, however (hence my interest in getting the final story mission, which awards a large number of marks...)