We use first-principles calculations to investigate the crystal and electronic structure of the hybrid bilayer-trilayer Ruddlesden-Popper (RP) nickelate La7Ni5O17 under hydrostatic pressure and biaxial compressive strain. By analyzing the irreducible representations of the dynamically unstable phonon modes in the high-symmetry P4/mmm structure, we identify a dynamically stable lower-symmetry C2/c structure containing octahedral tilts. The application of both pressure and compressive strain tends to suppress the octahedral tilts, effectively tetragonalizing the structure, in analogy with the conventional RPs. The electronic structure under hydrostatic pressure and strain has similarities, but it also shows significant band shifts. These strain-induced modifications mirror the electronic structure changes observed in the conventional bilayer nickelate.