  We present results of a search for continuously-emitted gravitational
radiation, directed at the brightest low-mass X-ray binary, Scorpius X-1. Our
semi-coherent analysis covers 10 days of LIGO S5 data ranging from 50-550 Hz,
and performs an incoherent sum of coherent $\mathcal{F}$-statistic power
distributed amongst frequency-modulated orbital sidebands. All candidates not
removed at the veto stage were found to be consistent with noise at a 1% false
alarm rate. We present Bayesian 95% confidence upper limits on
gravitational-wave strain amplitude using two different prior distributions: a
standard one, with no a priori assumptions about the orientation of Scorpius
X-1; and an angle-restricted one, using a prior derived from electromagnetic
observations. Median strain upper limits of 1.3e-24 and 8e-25 are reported at
150 Hz for the standard and angle-restricted searches respectively. This proof
of principle analysis was limited to a short observation time by unknown
effects of accretion on the intrinsic spin frequency of the neutron star, but
improves upon previous upper limits by factors of ~1.4 for the standard, and
2.3 for the angle-restricted search at the sensitive region of the detector.
