Two-dimensional (2D) materials with versatile properties are promising for diverse applications. In this work, a new family of 2D pentagonal NbX (penta-NbX, X = S, Se or Te) monolayers are designed to achieve the objectives. We demonstrate that these new materials are stable against mechanical strains, lattice dynamics and thermal fluctuations, because of the co-existence of ionic and covalent bonding between the Nb and X elements in these materials. We find that penta-NbX changes from metal to semiconductor as X changes from S/Se to Te. We show that penta-NbTe is a direct band-gap semiconductor with ultra-high carrier mobility (in the order of ~10⁴ cm² V⁻¹ s⁻¹), which is higher than or comparable to that of most 2D semiconductors and promising for ultra-fast electronics. We further show that metallic penta-NbS are catalytically active for hydrogen evolution reaction because of its low overpotential over a wide range of hydrogen coverages. We expect that the penta-NbX monolayers may find applications in electronics and electrocatalysis.