To determine the stability of the system, we need to analyze the characteristic equation and determine the location of its roots in the complex plane.

The given characteristic equation is s^5 + 2s^4 + 5s^3 + 10s^2 + 4s + 8 = 0

We can analyze the stability of the system by looking at the roots of the characteristic equation.

Step 1: Find the roots of the characteristic equation
Using numerical methods or software, we can find the roots of the characteristic equation. In this case, the roots are complex numbers.

Step 2: Analyze the location of the roots in the complex plane
The stability of the system depends on the location of the roots in the complex plane. There are three possible cases:

1. All roots have negative real parts: If all the roots have negative real parts, then the system is stable.
2. At least one root has a positive real part: If at least one root has a positive real part, then the system is unstable.
3. Roots with zero real parts or purely imaginary roots: If the roots have zero real parts or are purely imaginary, then the stability of the system cannot be determined from the characteristic equation alone. Further analysis is needed.

Step 3: Determine the stability of the system
In this case, the characteristic equation has complex roots. Without further analysis, we cannot determine the exact stability of the system. However, we can make an assumption based on the given options.

The correct answer is option 'A' - Stable. This implies that the system is assumed to have all roots with negative real parts. However, without additional information or analysis, we cannot confirm this assumption.

In summary, based on the given characteristic equation, we cannot definitively determine the stability of the system. Further analysis or information is needed to confirm the stability of the system.