I think that would be awesome to see in Avengers5. After all, in addition to being a S.H.I.E.L.D. agent, she's also fought alongside Earth's Mightiest Heroes in the comics under said code name.
about Mockingbird; not sure if that identity been introduced.
about being a SHIELD agent; she and Lance Hunter resigned in season 3.
about 5th Avengers; I imagine that it and 6th Avengers would only have characters that appeared in (and survived) previously released productions of Phases 4 through 6. at least the movies of those Phases; maybe also the shows.