We demonstrate that femtosecond laser pulses allow triggering high-frequency standing spin-wave modes in nanoscale thin films of a bismuth-substituted yttrium iron garnet. By varying the strength of the external magnetic field, we prove that two distinct branches of the dispersion relation are excited for all the modes. This is reflected in particular at a very weak magnetic field (∼33 mT) by a spin dynamics with a frequency up to 15 GHz, which is 15 times higher than the one associated with the ferromagnetic resonance mode. We argue that this phenomenon is triggered by ultrafast changes of the magnetic anisotropy via laser excitation of incoherent and coherent phonons. These findings open exciting prospects for ultrafast photo magnonics.