I have a trail rig that I am goign to run 31x10.5 r15 tires on. I have two of them. i also have 3 265/75/r15's. Can I run these different tires together? Thanks!

 

Hmmm. I never tried to run 5 tires before. I don't think it will work without some serious fabbing. Just kiddin'.
Seriously, I am not sure about the calculation comparison. But I do know if you run mismatched tires, they need to be close in diameter if you are going to put it in 4wd. I am talking like 1/2" or less. It really is not a good idea. Imagine both differentials trying to turn at the same speed, but the tires are fighting because of the circumference difference. One set would be traveling farther with every rotation than the other set. Big binding. No good.
If you want to check for difference yourself without all the math, put a string around each tire and see how close they really are.

 

if you are running 2wd it would be no problem as long as the same tires are on the same axle. but if you put different tires on the same axle, or go into 4wd, you're asking for problems

 

Which brand/model tires? What are their rolling diameters (available on tirerack.com or the mfg website)

2WD no problem
4WD on high traction surfaces (pavement, rock) will be a problem.
4WD on low traction surfaces (mud, sand) will probably be OK if the diameter difference is minimal