Average rainfall over the first four days: 0.40 inches Total rainfall over the first four days: $0.40$ inches/day $\times$ $4$ days = $1.60$ inches Average rainfall over six days: 0.50 inches Total rainfall over six days: $0.50$ inches/day $\times$ $6$ days = $3.00$ inches Total rainfall over the last two days: $3.00$ inches (total for six days) - $1.60$ inches (total for first four days) = $1.40$ inches Rainfall ratio on the fifth and sixth days: $4:3$ Let the rainfall on the fifth day be $4x$ and on the sixth day be $3x$.

Therefore:

Total rainfall over the last two days: $4x + 3x = 7x$ Since the total rainfall over the last two days is $1.40$ inches:

$7x = 1.40$ inches

Solving for $x$:

$x = \frac{1.40 \text{ inches}}{7}$

$x = 0.20$ inches

Thus, the rainfall on the fifth day is:

$4x = 4 \times 0.20$ inches = $0.80$ inches

Therefore, the rainfall on the fifth day was $0.80$ inches.