Localized coherent structures in high-dimensional quasicrystalline systems are investigated by employing the spectral renormalization method. In particular, a three-dimensional cubic-quintic nonlinear Schrödinger equation with a quasi-periodic potential is considered, and stationary soliton solutions of the system are obtained numerically. For two-dimensional quasicrystalline lattices with different rotational symmetries, the steady-state lattice solitons are systematically calculated, and their existence regions, spatial profiles, and power characteristics are analyzed in detail. Numerical results show that the peak amplitude of the soliton increases monotonically with the propagation constant, while the spatial width decreases accordingly, indicating stronger localization of the wave field. In addition, the confinement effect of the quasi-periodic potential becomes more pronounced as the rotational symmetry of the quasicrystal increases. The stability of the obtained solitons is further analyzed using the Vakhitov-Kolokolov stability criterion. For quasicrystalline lattices with fivefold rotational symmetry, the power-propagation constant curve remains monotonic within the considered parameter range, suggesting that the corresponding soliton family satisfies the stability condition. However, when the symmetry order exceeds fivefold, the power-propagation constant curves exhibit turning points, which imply that the interplay between nonlinearity and quasi-periodic lattice structures may introduce new instability mechanisms. To further verify the stability properties, direct numerical simulations are performed near these critical regions. The results confirm that the solitons can remain dynamically stable during propagation despite the presence of extreme points in the power curves. This demonstrates that the cubic-quintic nonlinearity together with the quasi-periodic potential can effectively support stable two-dimensional spatial solitons. The present study provides a theoretical basis for the manipulation and control of localized optical states in quasicrystalline photonic systems. Moreover, the proposed numerical approach does not rely on specific lattice symmetry and can be extended to aperiodic systems with various rotational symmetries, showing good generality and applicability.