1. Let the momenta of bodies $A$ and $B$ be $p_A$ and $p_B$ respectively.

   Given: $p_B = 2p_A$

2. Kinetic energy in terms of momentum is: $K = \frac{p^2}{2m}$

3. So for body $A$: $K_A = \frac{p_A^2}{2m_A} = \frac{p_A^2}{2\cdot 5} = \frac{p_A^2}{10}$

4. For body $B$: $K_B = \frac{p_B^2}{2m_B} = \frac{(2p_A)^2}{2\cdot 8} = \frac{4p_A^2}{16} = \frac{p_A^2}{4}$

5. Now find the ratio: $K_A : K_B = \frac{p_A^2}{10} : \frac{p_A^2}{4} = \frac{1}{10} : \frac{1}{4}$

   Multiply both terms by $20$: $K_A : K_B = 2 : 5$

6. Therefore, the ratio of their kinetic energies is: $\boxed{2:5}$

7. Checking options:

   • A: $4:5$ ❌
   • B: $2:5$ ✅
   • C: $5:4$ ❌
   • D: $5:2$ ❌

Hence, the correct option is B.