The given sequence is an arithmetic progression (AP), where the first term $a = 5$ and the common difference $d = 3$ (since $8 - 5 = 3$).

The formula to find the sum of the first $n$ terms of an arithmetic progression is:

$S_n = \frac{n}{2} \times (2a + (n - 1) d)$

Given $n = 15$, $a = 5$, and $d = 3$, we can substitute these values into the formula:

$S_{15} = \frac{15}{2} \times (2 \times 5 + (15 - 1) \times 3)$

Simplify:

$S_{15} = \frac{15}{2} \times (10 + 42) = \frac{15}{2} \times 52 = 15 \times 26 = 390$

Thus, the sum of the first 15 terms is $S_{15} = 390$.

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you find the sum of a different arithmetic sequence, such as 7 + 10 + 13 + ... up to 20 terms?
2. What is the 15th term in the sequence 5, 8, 11, 14, ...?
3. Can you calculate the sum of the first 50 terms in an arithmetic progression?
4. How do you determine the common difference in an arithmetic sequence if it's not given explicitly?
5. How can you find the number of terms required for the sum of an arithmetic progression to exceed a certain value?

Tip: To quickly identify an arithmetic sequence, check if the difference between consecutive terms is constant.