Several X-ray PhotoElectron Emission spectroMicroscopes (X-PEEMs) exist around the world at this time. We present recent performance and resolution tests of one of them, the Spectromicroscope for PHotoelectron Imaging of Nanostructures with X-rays (SPHINX) X-PEEM, installed at the University of Wisconsin Synchrotron Radiation Center. With this state-of-the-art instrument we demonstrate chemical analysis capabilities on conducting and insulating specimens of diverse interests, and an unprecedented lateral resolution of 10nm with monochromatic X-rays and 7.2nm with ultraviolet illumination.