  We report the results of a five-year survey of the northern sky to search for
point sources of high energy neutrinos. The search was performed on the data
collected with the AMANDA-II neutrino telescope in the years 2000 to 2004, with
a live-time of 1001 days. The sample of selected events consists of 4282 upward
going muon tracks with high reconstruction quality and an energy larger than
about 100 GeV. We found no indication of point sources of neutrinos and set 90%
confidence level flux upper limits for an all-sky search and also for a catalog
of 32 selected sources. For the all-sky search, our average (over declination
and right ascension) experimentally observed upper limit
\Phi^{0}=(E/TeV)^\gamma d\Phi/dE to a point source flux of muon and tau
neutrino (detected as muons arising from taus) is \Phi_{\nu_\mu}^{0} +
\Phi_{\nu_\tau}^{0} = 11.1 x 10^{-11} TeV^-1 cm^-2 s^-1, in the energy range
between 1.6 TeV and 2.5 PeV for a flavor ratio \Phi_{\nu_\mu}^{0} /
\Phi_{\nu_\tau}^{0}= 1 and assuming a spectral index \gamma=2. It should be
noticed that this is the first time we set upper limits to the flux of muon and
tau neutrinos. In previous papers we provided muon neutrino upper limits only
neglecting the sensitivity to a signal from tau neutrinos, which improves the
limits by 10% to 16%. The value of the average upper limit presented in this
work corresponds to twice the limit on the muon neutrino flux
\Phi_{\nu_\mu}^{0} = 5.5 \cdot 10^{-11} TeV^-1 cm^-2 s^-1. A stacking analysis
for preselected active galactic nuclei and a search based on the angular
separation of the events were also performed. We report the most stringent flux
upper limits to date, including the results of a detailed assessment of
systematic uncertainties.
