In an arithmetic sequence, the \( n \)-th term can be calculated using the formula:
\[ a_n = a_1 + (n - 1) \cdot d \]
Where:
- \( a_n \) is the \( n \)-th term,
- \( a_1 \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.
Given:
- \( a_1 = 5 \)
- \( d = 6 \)
- \( n = 13 \)
We can substitute these values into the formula:
\[ a_{13} = 5 + (13 - 1) \cdot 6 \]
Calculating \( (13 - 1) \):
\[ 13 - 1 = 12 \]
Now substitute this value back into the equation:
\[ a_{13} = 5 + 12 \cdot 6 \]
Calculating \( 12 \cdot 6 \):
\[ 12 \cdot 6 = 72 \]
Now add this to the first term:
\[ a_{13} = 5 + 72 = 77 \]
Thus, the 13th term of the arithmetic sequence is:
\[ \boxed{77} \]