Detailed chemical abundances for five stars in two Galactic globular clusters, NGC 5466 and NGC 5024, are presented from high-resolution optical (from the Hobby-Eberley Telescope) and infrared spectra (from the SDSS-III APOGEE survey). We find [Fe/H]=-1.97+/-0.13 dex for NGC 5466, and [Fe/H]=-2.06+/-0.13 dex for NGC 5024, and the typical abundance pattern for globular clusters for the remaining elements, e.g. both show evidence for mixing in their light element abundance ratios (C, N), and asymptotic giant branch contributions in their heavy element abundances (Y, Ba, and Eu). These clusters were selected to examine chemical trends that may correlate them with the Sgr dwarf galaxy remnant, but at these low metallicities no obvious differences from the Galactic abundance pattern are found. Regardless, we compare our results from the optical and infrared analyses to find that oxygen and silicon abundances determined from the infrared spectral lines are in better agreement with the other {alpha}-element ratios and with smaller random errors.