here's a list of candidates for 16x5 wheels.. LT type and heavier weight capacity are going to be difficult to find that small but several suitable radials for average daily driving..
click on specs for
rim diameter measured and
rim width ranges
these run approx 28" diameter and the light truck/suv apps are at the bottom, cooper, firestone, etc. under $150/ea
ALL TIRES FOR 195/75R16
here's a 205/80 that's 29" tall and off road type tread that fits 5-7.5 rims $162/ea - again may not be LT rated for weight capacity but DOT legal for on highway
Vredestein GRIP CLASSIC - SIZE: 205R16 On-/Off-Road All-Terrain
you can go through all 16" sizes and you may find something more to your liking - good luck!
https://www.tirerack.com/tires/sizes...sp?diameter=16