1. The problem is to evaluate the expression $\frac{5}{4} : 0.8$. 2. Division of a fraction by a number can be rewritten as multiplication by the reciprocal: $\frac{5}{4} : 0.8 = \frac{5}{4} \times \frac{1}{0.8}$. 3. Convert $0.8$ to a fraction: $0.8 = \frac{8}{10} = \frac{4}{5}$. 4. So, $\frac{1}{0.8} = \frac{1}{\frac{4}{5}} = \frac{5}{4}$. 5. Now multiply: $\frac{5}{4} \times \frac{5}{4} = \frac{25}{16}$. 6. The final answer is $\frac{25}{16}$ or as a decimal $1.5625$.