The fuel rod bundles are the core part of pressurized water reactors (PWRs), and its heat transfer characteristics directly impact the safety of PWRs. A computational fluid dynamics (CFD) model of 5 x 5 fuel rod bundles with a spacer grid is established, and the numerical simulation results are in excellent agreement with the experimental results. Then, the effects of four turbulence models, namely shear stress transport model, standard k-epsilon model, re-normalization group k-epsilon model, and realizable k-epsilon model on the thermal-hydraulic characteristics of the 5 x 5 fuel rod bundles are systematically investigated. Furthermore, two data-driven methods, namely proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are used to analyze the flow fields of the 5 x 5 fuel rod bundles. The two methods can extract key modes or features to enhance the comprehension and description of the dynamic behaviors within the flow fields of 5 x 5 fuel rod bundles. Finally, two reduced-order models (ROMs), called the POD-radial basis function neural network surrogate model and DMD method, are constructed, which can enable rapid prediction of the flow fields for 5 x 5 fuel rod bundles with high accuracy. The CFD simulation results presented in this paper can provide valuable insights for studying the thermal-hydraulic characteristics of the 5 x 5 fuel rod bundles. The two ROMs proposed in this paper can significantly reduce the computational costs associated with studying the thermal-hydraulic characteristics of 5 x 5 fuel rod bundles.