We present a comprehensive abundance analysis of 27 heavy elements in bright giant stars of the globular clusters M4 and M5 based on high-resolution, high signal-to-noise ratio spectra obtained with the Magellan Clay Telescope. We confirm and expand on previous results for these clusters by showing that (1) all elements heavier than, and including, Si have constant abundances within each cluster, (2) the elements from Ca to Ni have indistinguishable compositions in M4 and M5, (3) Si, Cu, Zn, and all s-process elements are approximately 0.3 dex overabundant in M4 relative to M5, and (4) the r-process elements Sm, Eu, Gd, and Th are slightly overabundant in M5 relative to M4. The cluster-to-cluster abundance differences for Cu and Zn are intriguing, especially in light of their uncertain nucleo-synthetic origins. We confirm that stars other than Type la supernovae must produce significant amounts of Cu and Zn at or below the clusters' metallicities. If intermediate-mass AGB stars or massive stars are responsible for the Cu and Zn enhancements in M4, the similar [Rb/Zr] ratios and (preliminary) Mg isotope ratios in both clusters may be problematic for either scenario. For the elements from Ba to Hf, we assume that the s- and r-process contributions are scaled versions of the solar s- and r-process abundances. We quantify the relative fractions of s- and r-process material for each cluster and show that they provide an excellent fit to the observed abundances.
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