To solve the expression \((0.8)^5 / (0.4)^6\), we can simplify it step by step.

First, let's rewrite the numbers in terms of fractions:
\[ 0.8 = \frac{8}{10} = \frac{4}{5} \]
\[ 0.4 = \frac{4}{10} = \frac{2}{5} \]

Now, substitute these fractions into the expression:
\[ \left( \frac{4}{5} \right)^5 / \left( \frac{2}{5} \right)^6 \]

Next, we can rewrite the division as a multiplication by the reciprocal:
\[ \left( \frac{4}{5} \right)^5 \times \left( \frac{5}{2} \right)^6 \]

Now, let's simplify each part separately:
\[ \left( \frac{4}{5} \right)^5 = \frac{4^5}{5^5} \]
\[ \left( \frac{5}{2} \right)^6 = \frac{5^6}{2^6} \]

So the expression becomes:
\[ \frac{4^5}{5^5} \times \frac{5^6}{2^6} \]

Combine the fractions:
\[ \frac{4^5 \times 5^6}{5^5 \times 2^6} \]

Since \(5^6 / 5^5 = 5\), we can simplify the expression:
\[ \frac{4^5 \times 5}{2^6} \]

Now calculate the powers:
\[ 4^5 = 1024 \]
\[ 2^6 = 64 \]

So the expression becomes:
\[ \frac{1024 \times 5}{64} \]

Multiply the numerator:
\[ 1024 \times 5 = 5120 \]

Now divide:
\[ \frac{5120}{64} = 80 \]

Therefore:
\[ \frac{(0.8)^5}{(0.4)^6} = 80 \]