The fluorescence quantum yield of Cy5 molecules attached to gold nanoparticles via ssDNA spacers is measured for Cy5-nanoparticle distances between 2 and 16 nm. Different numbers of ssDNA per nanoparticle allow to fine-tune the distance. The change of the radiative and nonradiative molecular decay rates with distance is determined using time-resolved photoluminescence spectroscopy. Remarkably, the distance dependent quantum efficiency is almost exclusively governed by the radiative rate.