We present an all-sky search for muon neutrinos produced during the prompt γ-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 γ-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.