We report the design and performance of a cryogen-free, pulse-tube refrigerator (PTR)-based scanning probe microscopy (SPM) system capable of operating at a base temperature of near 5 K. We achieve this by combining a home-made interface design between the PTR cold head and the SPM head, with an automatic gas-handling system. The interface design isolates the PTR vibrations by a combination of polytetrafluoroethylene and stainless-steel bellows and by placing the SPM head on a passive vibration isolation table via two cold stages that are connected to thermal radiation shields using copper heat links. The gas-handling system regulates the helium heat-exchange gas pressures, facilitating both the cooldown to and maintenance of the base temperature. We discuss the effects of each component using measured vibration, current-noise, temperature, and pressure data. We demonstrate that our SPM system performance is comparable to known liquid-helium-based systems with the measurements of the superconducting gap spectrum of Pb, atomic-resolution scanning tunneling microscopy image and quasiparticle interference pattern of Au(111) surface, and non-contact atomic force microscopy image of NaCl(100) surface. Without the need for cryogen refills, the present SPM system enables uninterrupted low-temperature measurements.