For the answer to the question above, I'll show my solution on how you can solve your problem.
AC² + BC² = AB²
5² + 12² = AB²
25 + 144 = AB²
169 = AB²
13 = AB
Triangle ABC is proportional to triangle ADB.
AC = AB
AB AD
5 = 13
13 AD
5AD = 169
AD = 169/5
AD = 33.8
AD = AC + CD
33.8 = 5 + CD
So the answer is
CD = 28.8