  We have carried out a Spitzer survey for brown dwarf (BD) disks in the ~5 Myr
old Upper Scorpius (UpSco) star forming region, using IRS spectroscopy from 8
to 12\mu m and MIPS photometry at 24\mu m. Our sample consists of 35 confirmed
very low mass members of UpSco. Thirteen objects in this sample show clear
excess flux at 24\mu m, explained by dust emission from a circum-sub-stellar
disk. Objects without excess emission either have no disks at all or disks with
inner opacity holes of at least ~5 AU radii. Our disk frequency of 37\pm 9% is
higher than what has been derived previously for K0-M5 stars in the same region
(on a 1.8 sigma confidence level), suggesting a mass-dependent disk lifetime in
UpSco. The clear distinction between objects with and without disks as well as
the lack of transition objects shows that disk dissipation inside 5 AU occurs
rapidly, probably on timescales of <~10^5 years. For the objects with disks,
most SEDs are uniformly flat with flux levels of a few mJy, well modeled as
emission from dusty disks affected by dust settling to the midplane, which also
provides indirect evidence for grain growth. The silicate feature around 10\mu
m is either absent or weak in our SEDs, arguing for a lack of hot, small dust
grains. Compared with younger objects in Taurus, BD disks in UpSco show less
flaring. Taken together, these results clearly demonstrate that we see disks in
an advanced evolutionary state: Dust settling and grain growth are ubiquituous
in circum-sub-stellar disks at ages of 5 Myr, arguing for planet forming
processes in BD disks. For almost all our targets, results from high-resolution
spectroscopy and high-spatial resolution imaging have been published before,
thus providing a large sample of BDs for which information about disks,
accretion, and binarity is available. (abridged)
