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Owing to its massive, dense core, Terzan 5 has the richest population of millisecond pulsars known among Galactic globular clusters. Here we report new deep $2-8\,$GHz radio continuum observations of Terzan\,5 obtained with the Karl G. Jansky Very Large Array. We have identified a total of 24 sources within the cluster half-light radius, including 17 within the core radius. 19 are associated with previously studied millisecond pulsars and X-ray binaries. Three of the new radio sources have steep radio spectra and are located within the cluster core, as expected for millisecond pulsars. These three sources have hard X-ray photon indices ($Γ=1.3-1.5$) and highly variable X-ray emission, suggesting they are binary millisecond pulsars belonging to the spider class. For the most X-ray luminous of these sources, the redback spider classification is confirmed by its X-ray light curve, which shows an orbital period of 12.32 hr and double peaked structure around X-ray maximum. The likely discovery of bright binary millisecond pulsars in a well-studied cluster like Terzan 5 highlights how deep radio continuum imaging can complement pulsar search and timing observations in finding probable eclipsing systems. The other new radio source in the core has a flat radio spectrum and is X-ray faint ($L_X \approx 2\times 10^{31}$ erg s$^{-1}$) with a photon index $Γ=2.1\pm0.5$, consistent with the properties expected for a quiescent stellar-mass black hole X-ray binary.