We present measurements of the neutron-capture elements Rb and Pb for bright giants in the globular clusters M4 and M5. The clusters are of similar metallicity ([Fe/ H] similar or equal to -1.2), but M4 is decidedly s-process enriched relative to M5: [Ba/Fe] = +0.6 for M4 but 0.0 for M5. The Rb and Pb abundances were derived by comparing synthetic spectra with high-resolution, high signal-to-noise ratio spectra obtained with MIKE on the Magellan Telescope. Abundances of Y, Zr, La, and Eu were also obtained. In M4, the mean abundances from 12 giants are [Rb/Fe] = 0.39 +/- 0.02 (sigma = 0.07), [Rb/Zr] = 0.17 +/- 0.03 (sigma = 0.08), and [Pb/Fe] = 0.30 +/- 0.02 (sigma = 0.07). In M5, the mean abundances from two giants are [Rb/Fe] = 0.00 +/- 0.05 (sigma = 0.06), [Rb/Zr] = 0.08 +/- 0: 08 (sigma = 0.11), and [Pb/Fe] = -0.35 +/- 0.02 (sigma = 0.04). Within the measurement uncertainties, the abundance ratios [Rb/Fe], [Pb/Fe], and [Rb/X] for X = Y, Zr, and La are constant from star to star in each cluster, and none of these ratios are correlated with O or Na abundances. While M4 has a higher Rb abundance than M5, the ratios [Rb/X] are similar in both clusters, indicating that the nature of the s-products is very similar for each cluster but the gas from which M4's stars formed had a higher concentration of these products
