  We present an all-sky search for muon neutrinos produced during the prompt
$\gamma$-ray emission of 1172 gamma-ray bursts (GRBs) with the IceCube Neutrino
Observatory. The detection of these neutrinos would constitute evidence for
ultra-high energy cosmic ray (UHECR) production in GRBs, as interactions
between accelerated protons and the prompt $\gamma$-ray field would yield
charged pions, which decay to neutrinos. A previously reported search for muon
neutrino tracks from Northern Hemisphere GRBs has been extended to include
three additional years of IceCube data. A search for such tracks from Southern
Hemisphere GRBs in five years of IceCube data has been introduced to enhance
our sensitivity to the highest energy neutrinos. No significant correlation
between neutrino events and observed GRBs is seen in the new data. Combining
this result with previous muon neutrino track searches and a search for cascade
signature events from all neutrino flavors, we obtain new constraints for
single-zone fireball models of GRB neutrino and UHECR production.
