We report on an all-sky search for periodic gravitational waves in the frequency band 50-800 Hz and with the frequency time derivative in the range of 0 through $-6\times 10^{-9} \text{ Hz}/\text{s}$. Such a signal could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy. After recent improvements in the search program that yielded a 10x increase in computational efficiency, we have searched in two years of data collected during LIGO's fifth science run and have obtained the most sensitive all-sky upper limits on gravitational wave strain to date. Near 150 Hz our upper limit on worst-case linearly polarized strain amplitude $h_0$ is $1\times 10^{-24}$, while at the high end of our frequency range we achieve a worst-case upper limit of $3.8\times 10^{-24}$ for all polarizations and sky locations. These results constitute a factor of two improvement upon previously published data. A new detection pipeline utilizing a Loosely Coherent algorithm was able to follow up weaker outliers, increasing the volume of space where signals can be detected by a factor of 10, but has not revealed any gravitational wave signals. The pipeline has been tested for robustness with respect to deviations from the model of an isolated neutron star, such as caused by a low-mass or long-period binary companion.