This is a Co-I proposal for the Antarctic Impulsive Transient Antenna (ANITA) mission (P. Gorham, Hawaii, PI). We propose to fly a significantly improved version of the Antarctic Impulsive Transient Antenna (ANITA) long-duraction balloon payload, with a goal of discovering and characterizing ultra-high energy (UHE) neutrinos and cosmic rays in the EeV (Exa-electronvolt) energy range and above. This will be the fifth flight of ANITA payloads, and should achieve the a milestone of 100 days of integrated livetime on orbit, proposed in the earliest flight as a goal for the application of ANITA's novel methodology. Each payload in the series has yielded improved sensitivity, and unexpected results, both in the form of upper limits that excluded long-held predictions for the isotropic neutrino flux from various models, and in the form of serendiptious detections of UHE cosmic rays via radio pulses that were not well understood when ANITA first flew. Moreover, ANITA's ability to perform precision measurements of the pulse shape and polarization properties of the UHE cosmic ray events led to the discovery of candidates for tau-lepton-generated air showers, one in the ANITA-I flight, and most recently, a second candidate in the ANITA-III flight. These events signal the possible appearance of a flux of UHE tau neutrinos, appearing with unexpected properties, in tension with other measurements. ANITA-V will provide an opportunity to elucidate these new potential signals in a compelling way with far-reaching implications for fundamental physics.