Lead halide perovskites are widely employed in photonic and light-emitting devices because of their rich optoelectronic properties and simplicity of fabrication based on low-cost flexible technologies. Perovskite bulk crystals and films demonstrate outstanding nonlinear characteristics with large optical nonlinearities exceeding the nonlinear susceptibilities of conventional semiconductor materials by several orders of magnitude. One of the promising approaches for further enhancement of the nonlinear response of perovskites as dielectric photonic materials is to employ optical resonances of structured surfaces, or metasurfaces. Nonlocal metasurfaces supporting lattice modes over many unit cells provide a new approach to both spatial and spectral control of light fields, and they may deliver improved characteristics of nonlinear effects for a wide range of applications associated with broadband excitation of multiple high-quality resonances. Here we report on the first observation of enhanced fifth harmonic generation in MAPbBr3 halide perovskite nonlocal metasurfaces driven by high-quality resonances at the generated harmonic wavelength in the visible frequency range. The demonstrated enhancement is about 2 orders of magnitude compared to an unpatterned MAPbBr3 film of the same thickness, and is broadband by virtue of the excitation of multiple resonant modes in the highly nonlocal regime. Our work suggests a novel approach for achieving parametric processes in resonant dielectric structures with high efficiency.