NuSTAR observed the bright Compton-thin, narrow-line Seyfert 1 galaxy, NGC 5506, for about 56 ks. In agreement with past observations, the spectrum is well fitted by a power law with G ~ 1.9, a distant reflection component and narrow ionized iron lines. A relativistically blurred reflection component is not required by the data. When an exponential high-energy cutoff is added to the power law, a value of 720 ... keV (90 per cent confidence level) is found. Even allowing for systematic uncertainties, we find a 3... lower limit to the high-energy cutoff of 350 keV, the highest lower limit to the cutoff energy found so far in an AGN by NuSTAR. (ProQuest: ... denotes formulae/symbols omitted.)