To evaluate the expression \( 5 - \frac{t}{3} \) when \( t = 12 \), we first substitute \( t \) with \( 12 \):
\[ 5 - \frac{12}{3} \]
Next, we calculate \( \frac{12}{3} \):
\[ \frac{12}{3} = 4 \]
Now we substitute this value back into the expression:
\[ 5 - 4 \]
Finally, we perform the subtraction:
\[ 5 - 4 = 1 \]
Thus, the value of the expression when \( t = 12 \) is
\[ \boxed{1} \]