Oh sure, there can be exceptions to specific roads in specific conditions.

So if OP had said they were turning left and therefore that's why they needed to be in the left lane, I would agree that TCA 55-8-204(b)(5) applied. Also, by its own terms, TCA 55-8-204 itself only applies on "interstate and multilane divided highways."

But that's not the only law that applies. See also TCA 55-8-115(b), which applies "upon all roadways":

(b) Upon all roadways any vehicle proceeding at less than the normal speed of traffic at the time and place and under the conditions then existing shall be driven in the right-hand lane then available for traffic, or as close as practicable to the right-hand curb or edge of the roadway, except when overtaking and passing another vehicle proceeding in the same direction or when preparing for a left turn at an intersection or into a private road or driveway.

Again, this law permits drivers to be in the left lane even if they are slower when they are already passing another vehicle or preparing to turn left.

My complaint with the above comment is that it is trying to say that the "slower traffic keep right" law doesn't apply if a road isn't a "highway," using some definition of highway that they have in their head. That is simply not true. All public roads are highways in Tennessee. In fact, Tennessee explicitly defines "highway" and "street" as meaning the same thing! See TCA 55-1-116:

"Highway" or "street" means the entire width between boundary lines of every way publicly maintained, when any part thereof is open to the use of the public for purposes of vehicular travel.