1.
A-5, B-10, C-2 = No, the length will not contruct a triangle
2.
A-8, B-2, C-10 = No, the length will not contruct a triangle
3.
A-13, B-15, C-23 = Yes, they can construct a triangle
4.
A-1, B-17, C-3 = No, the length will not contruct a triangle
5.
A-33, B-30, C-21 = Yes, they can construct a triangle
I really don't know how to explain how I got these answers, but the rule is The Triangle Inequality Theorem. It states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. The picture below should hopefully help.