What is the length of the longest side of a triangle that has vertices at (-5, -1), (-5, 5), and (3, -1)?

First check to see if you have a triangle at all. Add the two short dimensions. If the sum is STRICTLY GREATER THAN the long side, then you have a triangle and you can proceed. (If the sum of the two short sides is equal to the third side, then you have a straight line -- not a triangle. If the sum of the two short sides is less than the third side, then you have two short sides flapping around unable to meet in a third vertex.)

Square the measures of each of the sides and then sum the squares of the two short sides.

If the sum is equal to the square of the long side, then you have a right triangle.