This paper considers the attitude determination problem based on the global navigation satellite system (GNSS) and fifth-generation (5G) measurement fusion to address the shortcomings of standalone GNSS and 5G techniques in deep urban regions. The tight fusion of the GNSS and the 5G observations results in a unique hybrid integer- and orthonormality-constrained optimization problem. To solve this problem, we propose an estimation method consisting of the steps of float solution computation, ambiguity resolution, and fixed solution computation. Numerical results reveal that the proposed method can effectively improve the attitude determination accuracy and reliability compared to either the pure GNSS solution or the pure 5G solution.