The gravitational-wave (GW) sky may include nearby pointlike sources as well as stochastic backgrounds. We perform two directional searches for persistent GWs using data from the LIGO S5 science run: one optimized for pointlike sources and one for arbitrary extended sources. Finding no evidence to support the detection of GWs, we present 90% confidence level (C.L.) upper-limit maps of GW strain power with typical values between 2 - 20 x 10-50 strain2 Hz-1 and 5 - 35 x 10-49 strain2Hz-1sr-1 for pointlike and extended sources, respectively. The latter result is the first of its kind. We also set 90% C.L. limits on the narrow-band root-mean-square GW strain from interesting targets including Sco X-1, SN 1987A and the Galactic center as low as ≈7 x 10-25 in the most sensitive frequency range near 160 Hz.