Thomas, yes Sir, the barrel is stamped 5.56 - Thompson Center lists this rifle as fine for both 5.56 and .223 so you are fine Sir : https://tcarms.com/firearms/bolt-action-rifles/venture/venture-ii

Tc's page does indeed say the barrel is 556, they likely call it a 223 rifle as it is designed and marketed for hunting. There are alot more hunting specific cartridges on 223 then there are 556. Just always check the barrel stamp, guns rated for 556 will almost always have stamped on the barrel.
"Caliber : 223/5.56
Finish/Stock : Weather Shield/Black Composite w/Hogue® Panels
Trigger : 3-4 lbs. GENERATION II
Barrel Length : 22"
Rate of Twist : 1:9
Capacity : 3+1 Det. Mag
Length of Pull : 13.5"
Overall Length : 42"
Weight : 7.4 lbs.
Sights : None"

Thomas, this gun is rated for 5.56, so you can shoot either 5.56 or 223 in this gun. Specs here--https://tcarms.com/firearms/bolt-action-rifles/venture/venture-ii