  The novel five-Penning trap mass spectrometer PENTATRAP is developed at the
Max-Planck-Institut f\"ur 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 \beta-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.
