Pentagraphyne (PG-yne), a recently predicted two-dimensional (2D) carbon allotrope with appealing properties, has opened up possibilities for a wide range of applications. In this study, we investigate the structural, electronic, optical, and electrical transport properties of a novel one-dimensional (1D) system called pentagraphyne nanotubes (PG-yneNTs), formed by rolling a PG-yne sheet, using density functional theory (DFT) calculations. We design PG-yneNTs with diameters ranging from 6.94 Å to 13.62 Å and employ state-of-the-art theoretical calculations to confirm their energetic, dynamic, and thermodynamic stability. Our electronic band structure calculations reveal that all these nanotubes are wide indirect band gap semiconductors. Remarkably, PG-yneNTs exhibit superior optical properties, including high absorption coefficients and absorption spectra covering the visible regime of the electromagnetic spectrum, making them potential candidates for visible-light-driven photocatalysis and solar cells. Interestingly, both the electronic and optical band gaps increase with the diameter of the nanotubes. Additionally, the observation of negative differential resistance (NDR) phenomena in (4, 0) PG-yneNT suggests their potential applications in NDR devices such as fast switches, frequency multipliers, and memory devices.