The magnetic properties of UCu5 with the C15b-type cubic crystal structure, which shows an antiferromagnetic transition at 15 K and, further, an unidentified transition at 1 K, were investigated by using the nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) techniques. The measurements were performed for both crystallographically inequivalent Cu sites with cubic and trigonal symmetry in all the paramagnetic, antiferromagnetic and unidentified states. The results clearly indicate that the low-temperature state below I K is another antiferromagnetic state with a different spin structure from the high-temperature state. From the temperature variation of the field-swept spectrum, we propose a non-collinear quadruple-q (4-q) structure for the state between 15 and 1 K, which is different from the structure previously proposed by Murasik et al based on their neutron diffraction result. Furthermore, we propose a collinear single-q (1-q) structure for the state below 1 K, which cannot be distinguished from the 4-q structure by neutron diffraction. Assuming a simple model for hyperfine interactions and the magnetic structures, we consistently explain the complicated zero-field spectra obtained both above and below 1 K. The analysis shows clearly the spin reorientation at 1 K and that the variation of the local field at Cu sites is reasonably interpreted in terms of only the spin reorientation. The analysis also indicates that the electric field gradient changes significantly at 1 K, which is in contrast to no change at 15 K. The relation between the spin reorientation and the gap formation at 1 K is discussed.