Context. It has recently been shown numerically that a small-scale dynamo (SSD) instability might be possible in solar-like low magnetic Prandtl number plasmas. It was proposed that the presence of SSD might have a significant effect on the dynamics of the large-scale dynamo (LSD) in stellar convection zones. The simultaneous study of these two dynamos, SSD and LSD, in a global magnetoconvection model requires high-resolution simulations and large amounts of computational resources. Aims. Starting from a well-studied global convective dynamo model that produces cyclic magnetic fields, we systematically increased the resolution and lowered the diffusivities to enter the regime of Reynolds numbers that enable the excitation of SSD in addition to the LSD. We studied the change in the properties of convection, generated differential rotation profiles, and LSD solutions due to the presence of SSD. Methods. We performed semiglobal convective dynamo simulations in a spherical wedge with the Pencil Code. The resolutions of the models were increased in four steps by a total factor of 16 to achieve maximum fluid and magnetic Reynolds numbers of above 500. Results. We found that differential rotation is strongly quenched by the presence of the LSD and SSD. Even though the small-scale magnetic field only mildly decreases with increasing Reynolds number, the large-scale field strength decreases significantly. We found no significant quenching of the convective flows by the SSD, as recently claimed by other authors; in contrast, the convective flows first grow and then saturate for increasing Reynolds numbers. Furthermore, the angular momentum transport is highly affected by the presence of small-scale magnetic fields, which are mostly generated by tangling of the LSD. These fields not only change the Reynolds stresses, but also generate dynamically important Maxwell stresses. The LSD evolution in terms of its pattern and field distribution is rather independent of the increase in the fluid and magnetic Reynolds numbers. Conclusions. At high fluid and magnetic Reynolds numbers, an SSD can be excited in addition to the LSD, and both strongly affect the angular momentum transport. Hence, it is important to study both dynamos and their interplay together to fully understand the dynamics of the Sun and other stars.