The X-ray mass attenuation coefficients of silver were measured in the energy range 5-20 keV with an accuracy of 0.01-0.2% on a relative scale down to 5.3 keV, and of 0.09-1.22% on an absolute scale to 5.0 keV. This analysis confirms that with careful choice of foil thickness and careful correction for systematics, especially including harmonic contents at lower energies, the X-ray attenuation of high-Z elements can be measured with high accuracy even at low X-ray energies (<6 keV). This is the first high-accuracy measurement of X-ray mass attenuation coefficients of silver in the low energy range, indicating the possibility of obtaining high-accuracy X-ray absorption fine structure down to the L1 edge (3.8 keV) of silver. Comparison of results reported here with an earlier data set optimized for higher energies confirms accuracy to within one standard error of each data set collected and analysed using the principles of the X-ray extended-range technique (XERT). Comparison with theory shows a slow divergence towards lower energies in this region away from absorption edges. The methodology developed can be used for the XAFS analysis of compounds and solutions to investigate structural features, bonding and coordination chemistry.