We present a search for near-infrared (3.5-5 mu m) emission from baryonic d
ark matter in the form of low-mass stars and/or brown dwarfs in the halo of
the nearby edge-on spiral galaxy NGC 5907. The observations were made usin
g a 256 x 256 InSb array with a pixel scale of 17" at the focus of a liquid
-helium-cooled telescope carried above the Earth's atmosphere by a sounding
rocket. In contrast to previous experiments that have detected a halo arou
nd NGC 5907 in the V, R, I, J, and K bands at galactic radii 6 kpc < r < 10
kpc, our search finds no evidence for emission from a halo at 10 kpc < r <
30 kpc. Assuming a halo mass density scaling as r(-2), which is consistent
with the flat rotation curves that are observed out to radii of 32 kpc, th
e lower limit of the mass-to-light ratio at 3.5-5 mu m for the halo of NGC
5907 is 250 (2 sigma) in solar units. This is comparable to the lower limit
we have found previously for NGC 4565. Based on recent models, our nondete
ction implies that hydrogen-burning stars contribute less than 15% of the m
ass of the dark halo of NGC 5907. Our results are consistent with the previ
ous detection of extended emission at r less than or equal to 10 kpc if the
latter is caused by a stellar population that has been ejected from the di
sk because of tidal interactions. We conclude that the dark halo of NGC 590
7, which is evident from rotation curves that extend far beyond 10 kpc, is
not made up of hydrogen-burning stars.