print(dir(xxxx)) is your friend. It displays all the next dot properties that are valid for the supplied variable.
>>> psys = ob.particle_systems[0]
>>> print(dir(psys))
['__doc__', '__module__', '__slots__', 'active_particle_target', 'active_particle_target_index', 'billboard_normal_uv', 'billboard_split_uv', 'billboard_time_index_uv', 'bl_rna', 'child_particles', 'child_seed', 'cloth', 'co_hair', 'dt_frac', 'has_multiple_caches', 'invert_vertex_group_clump', 'invert_vertex_group_density', 'invert_vertex_group_field', 'invert_vertex_group_kink', 'invert_vertex_group_length', 'invert_vertex_group_rotation', 'invert_vertex_group_roughness_1', 'invert_vertex_group_roughness_2', 'invert_vertex_group_roughness_end', 'invert_vertex_group_size', 'invert_vertex_group_tangent', 'invert_vertex_group_velocity', 'is_editable', 'is_edited', 'is_global_hair', 'mcol_on_emitter', 'name', 'parent', 'particles', 'point_cache', 'reactor_target_object', 'reactor_target_particle_system', 'rna_type', 'seed', 'set_resolution', 'settings', 'targets', 'use_hair_dynamics', 'use_keyed_timing', 'uv_on_emitter', 'vertex_group_clump', 'vertex_group_density', 'vertex_group_field', 'vertex_group_kink', 'vertex_group_length', 'vertex_group_rotation', 'vertex_group_roughness_1', 'vertex_group_roughness_2', 'vertex_group_roughness_end', 'vertex_group_size', 'vertex_group_tangent', 'vertex_group_velocity']
So try.
ob.particle_systems[0].settings.count = 5