It is well-established that the magnitude of the incident stellar flux is the single most important factor in determining the day-night temperature gradients and atmospheric chemistries of short-period gas giant planets. However it is likely that other factors, such as planet-to-planet variations in atmospheric metallicity, C/O ratio, and cloud properties, also contribute to the observed diversity of infrared spectra for this population of planets. In this study we present new 3.6 and 4.5 micron secondary eclipse measurements for five transiting gas giant planets: HAT-P-5b, HAT-P-38b, WASP-7b, WASP-72b, and WASP-127b. We detect eclipses in at least one bandpass for all five planets and confirm circular orbits for all planets except for WASP-7b, which shows evidence for a non-zero eccentricity. Building on the work of Garhart et al. ( 2020), we place these new planets into a broader context by comparing them with the sample of all planets with measured Spitzer secondary eclipses. We find that incident flux is the single most important factor for determining the atmospheric chemistry and circulation patterns of short-period gas giant planets. Although we might also expect surface gravity and host star metallicity to play a secondary role, we find no evidence for correlations with either of these two variables.