  No simulation of intense beam transport has accurately reproduced
measurements at the level of beam halo. One potential explanation of this
discrepancy is a lack of knowledge of the initial distribution of particles in
six-dimensional (6D)~phase space. A direct 6D measurement of an ion beam was
recently performed at the Spallation Neutron Source (SNS) Beam Test Facility
(BTF), revealing nonlinear transverse-longitudinal correlations in the beam
core that affect downstream evolution. Unfortunately, direct 6D~measurements
are limited in resolution and dynamic range; here, we discuss the use of three
slits and one screen to measure a 5D projection of the 6D phase space
distribution, overcoming these limitations at the cost of one dimension. We
examine the measured 5D distribution before and after transport through the BTF
and compare to particle-in-cell simulations. We also discuss the possibility of
reconstructing the 6D distribution from 5D and 4D projections.
