Let's call the side BD Z and the angle ACD X and the angle CDA W, you can observe that those triangles have the same angles : X,W and 90. That implies:
[tex] \frac{z}{6} = \frac{5}{z} \\ \\ z {}^{2} = 30 \\ \\ y {}^{2} = z {}^{2} + 5 {}^{2} \\ \\ y = \sqrt{30 + 25} \\ \\ y = \sqrt{55} [/tex]
