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The origin of GeV emission from the early epoch of gamma-ray bursts (GRBs) is a widely discussed issue. The long gamma-ray burst GRB 170405A, observed by the Fermi Gamma-ray Space Telescope showed high-energy emission delayed by $\sim$20 s with respect to the X-ray emission, followed by temporally fading gamma-ray emission lasting for $\sim$1,000 s, as commonly observed in high-energy GRBs. In addition, a high-energy spectral cutoff at $\sim$50 MeV was detected in the prompt emission phase. If this feature is caused by pair-production opacity, the bulk Lorentz factor of the GRB ejecta can be estimated to be $Γ_{\rm bulk}$ = 170-420. Simultaneously with Fermi, GRB 170405A was observed by Swift/Burst Alert Telescope (BAT) and X-ray telescope (XRT), and a clear optical onset was detected $\sim$200 s after the burst by Swift/UltraViolet Optical Telescope (UVOT). By coupling the deceleration time to the derived bulk Lorentz factor, the deceleration time was found to correspond to the delayed onset in the optical band. While the delayed onset in the optical band is evidence that this emission had an external shock origin, the temporally extended emission in the GeV band before the optical onset is hard to reconcile with the standard synchrotron emission from the same external shock. This may imply that the common feature of GeV emission with a power-law decay does not necessarily have the same origin of the optical afterglow in all Fermi/LAT GRBs, particularly in their early epoch. Another emission mechanism to explain the GeV emission in GRB 170405A can be required such as an internal-shock or inverse Compton emission.