As I understand it, the 5W or 10W viscosity is at "freezing" and the upper viscosity rating is for engine operating temperatures (basically, 180-190 degrees F). IF that definition is correct, the lower number in the somewhat warmer TX weather (except for this week!) is not that sensitive to needing the 5W-20 viscosities compared to 10W-30, yet the 5W-20 oil would probably flow a bit easier during warmup (meaning less power consumed by the engine's oil pump and possiby better fuel economy in THAT particular operational mode).
In prior times with earlier oils, I would think that anything less than an upper number of "30" would not work in the southwestern USA summer months, but things have improved considerably since that time. In those prior times, some OEMs recommended 10W-40 or 20W-50 oil for those hotter climates in the summer. That was then, this is now.
Enjoy!
CBODY67