To determine if three side lengths can form a triangle, we apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

For the side lengths 5, 7, and 13, we need to check the following inequalities:

1. $5 + 7 > 13$
2. $5 + 13 > 7$
3. $7 + 13 > 5$

Let's check:

1. $5 + 7 = 12$, which is not greater than 13.
2. $5 + 13 = 18$, which is greater than 7.
3. $7 + 13 = 20$, which is greater than 5.

Since the first inequality fails ($5 + 7$ is not greater than 13), these side lengths cannot represent a triangle.

Would you like to explore more about triangle inequalities or test other sets of side lengths? Here are some related questions:

1. How does the triangle inequality work for right-angled triangles?
2. Can a set of side lengths form a degenerate triangle?
3. What are some ways to verify if a set of side lengths can form an obtuse triangle?
4. What are the conditions for an equilateral triangle?
5. How do you calculate the area of a triangle given three sides?

Tip: The triangle inequality is crucial when determining the possibility of forming a triangle. Always test the sums of each pair of sides!