What is the length of BD?

In a rectangle, the diagonals are equal in length and bisect each other. This means that the point where the diagonals intersect (O) divides each diagonal into two equal parts. Also, all four segments from the center to each vertex are equal in length.
So, $AO = OC = BO = OD$.

We are given that $AO = 5$ cm.
Since $AO = OC$, the full length of diagonal $AC$ is $AO + OC = 5 \text{ cm} + 5 \text{ cm} = 10 \text{ cm}$.

Because the diagonals of a rectangle are equal in length, $BD = AC$.
Therefore, $BD = 10$ cm.

The length of BD is $\text{B. 10 cm}$.