How do i find the missing length if the triangle?

Use the pythagorean theorem which works for right triangles. Its a squared + b squared=c squared. c is 13 since that's the length of the side opposite of the right angle so its the hypotenuse which is c. 5 is a leg. Plug them in.
(5) squared + bsquared=(13) squared
Simplify.
25+bsquared=169
subtract 25 from both sides 
b squared equals 144
find square root of both sides
b=12