Solve the equation. \( \frac{1}{3}(9 t-5)=\frac{t+5}{6} \)

To solve the equation \( \frac{1}{3}(9 t-5)=\frac{t+5}{6} \), we first eliminate the fractions by finding a common denominator. The common denominator for 3 and 6 is 6, so we multiply both sides by 6: \[ 6 \cdot \frac{1}{3}(9t - 5) = 6 \cdot \frac{t + 5}{6}. \] This simplifies to: \[ 2(9t - 5) = t + 5. \] Now distribute on the left side: \[ 18t - 10 = t + 5. \] Next, we move the \( t \) term on the right side to the left side by subtracting \( t \) from both sides: \[ 18t - t - 10 = 5, \] which simplifies to: \[ 17t - 10 = 5. \] Then, we add 10 to both sides: \[ 17t = 15. \] Finally, we divide both sides by 17 to isolate \( t \): \[ t = \frac{15}{17}. \] So the solution to the equation is: \[ t = \frac{15}{17}. \]