To simplify the expression \(\frac{\sqrt{8} - \sqrt{3}}{\sqrt{8} + \sqrt{3}}\), follow these steps:

1. Rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:
\[
\frac{\sqrt{8} - \sqrt{3}}{\sqrt{8} + \sqrt{3}} \times \frac{\sqrt{8} - \sqrt{3}}{\sqrt{8} - \sqrt{3}}
\]

2. Multiply the numerators and the denominators:
\[
\text{Numerator:} \quad (\sqrt{8} - \sqrt{3})(\sqrt{8} - \sqrt{3})
\]
\[
\text{Denominator:} \quad (\sqrt{8} + \sqrt{3})(\sqrt{8} - \sqrt{3})
\]

3. Expand both parts:
- Numerator:
\[
(\sqrt{8})^2 - 2 \cdot \sqrt{8} \cdot \sqrt{3} + (\sqrt{3})^2 = 8 - 2 \cdot \sqrt{24} + 3 = 8 - 2 \cdot 2\sqrt{6} + 3 = 11 - 4\sqrt{6}
\]
- Denominator (difference of squares formula):
\[
(\sqrt{8})^2 - (\sqrt{3})^2 = 8 - 3 = 5
\]

4. Combine the results:
\[
\frac{11 - 4\sqrt{6}}{5}
\]

So, the simplified expression is \(\frac{11 - 4\sqrt{6}}{5}\).

The correct answer is B. \(\frac{11 - 4\sqrt{6}}{5}\).