Find the sum of the first 13 terms of the geometric sequence with first term 5 and common ratio 2 . $s_{13}=\square$ (Simplify your answer.)

Step 1 ：Define the first term (a) as 5, the common ratio (r) as 2, and the number of terms (n) as 13.

Step 2 ：Use the formula for the sum of a geometric sequence, which is \(S_n = a \cdot \frac{r^n - 1}{r - 1}\).

Step 3 ：Substitute the values into the formula: \(S_{13} = 5 \cdot \frac{2^{13} - 1}{2 - 1}\).

Step 4 ：Simplify the expression to find that \(S_{13} = 40955.0\).

Step 5 ：Final Answer: The sum of the first 13 terms of the geometric sequence with first term 5 and common ratio 2 is \(\boxed{40955}\).