The novel five-Penning trap mass spectrometer Pentatrap is developed at the Max-Planck-Institut für Kernphysik (MPIK), Heidelberg. Ions of interest are long-lived highly charged nuclides up to bare uranium. Pentatrap aims for an accuracy of a few parts in 10 12 for mass ratios of mass doublets. A physics program for Pentatrap includes Q-values measurements of β-transitions relevant for neutrino physics, stringent tests of quantum electrodynamics in the regime of extreme electric fields, and a test of special relativity. Main features of Pentatrap are an access to a source of highly charged ions, a multi-trap configuration, simultaneous measurements of frequencies, a continuous precise monitoring of magnetic field fluctuations, a fast exchange between different ions, and a highly sensitive cryogenic non-destructive detection system. This paper gives a motivation for the new mass spectrometer Pentatrap, presents its experimental setup, and describes the present status.