Question

It’s possible to build a triangle with side lengths of 5,5, and 10

Answer 1

No.  The two lengths 5 and 5 add up to 10; you'd have two sides of length 5 each placed end to end, equaling 10.  That'd be represented by segments on a straight line, not a triangle.

Hope you've drawn a picture, so as to understand this better.  ;)

Answer 2

No, as two sides (5 and 5) added together would equal 10. A triangle made with sides like that would just turn into a straight line.